Traditional actuarial techniques have long been employed in the insurance industry for pricing, underwriting, and loss reserving. These methods typically rely on historical data and well-established statistical models. However, they come with several limitations: Traditional actuarial models often depend heavily on assumptions about the distribution of data, which may not hold true in real-world scenarios [10] . These models are usually static, meaning they do not adapt well to rapidly changing environments or emerging risks [11] . Traditional methods struggle with the vast amounts of data generated in modern insurance practices and are not well-equipped to handle unstructured data [12] . The actuarial process often involves significant manual processing, making it time-consuming and prone to human error [13] .

Recent advancements in machine learning (ML) have introduced more dynamic and adaptable methods for insurance practices, addressing some of the limitations of traditional techniques. These approaches offer several advantages: ML algorithms can process and learn from large datasets, providing more accurate and granular insights [14] . These models can adapt to new data and changing conditions, making them more resilient to evolving risk landscapes [15] . ML models automate much of the data processing and analysis, reducing the potential for human error and increasing efficiency [16] .

GLMs have been widely used for predicting insurance losses. They offer flexibility and robustness in handling different types of data [17] . GBMs have been employed to enhance prediction accuracy by combining multiple weak prediction models [18] . [19] explored the use of neural networks for claims reserving, demonstrating their ability to capture complex non-linear relationships in the data. SVMs have been used for classification tasks in insurance pricing, offering high accuracy in identifying risk categories [20] . Random Forests have been applied to pricing models to improve prediction accuracy by aggregating multiple decision trees [9] .

Logistic regression models have been used for underwriting decisions, particularly in assessing the probability of claim events [21] . XGBoost, a scalable tree boosting system, has been shown to enhance underwriting models by efficiently handling large datasets and improving prediction accuracy [22] .

[23] came with his study on the Risk Premium Prediction of Car Damage Insurance using Artificial Neural Networks and Generalized Linear Models. The two methods were used in insurance pricing prediction and upon his study the Artificial Neural Networks proved to be more precise and accurate than the Generalized linear models.

[24] conducted the research on Data analytics for insurance loss modeling, telematics pricing and claims reserving. In his thesis credible innovations to the insurance loss modeling, pricing and claims reserving for the general automobile general insurance data were put in place however lack of the use and application of Artificial intelligence in his research resulted in his study entirely based on traditional statistical methods particularly the parametric methods.

[25] carried out a research on the Non-life insurance rate making techniques. Their study was based on the customary actuarial distinction between the two main pricing techniques, namely the prior and the posterior rate making techniques. [26] carried out a study on Machine Learning and Traditional Methods Synergy in Non-Life reserving. This group of researchers looked at both traditional and machine based methods such as ANNs, Trees and Boosted Tweddie compound poison model. In addition to that their research was entirely on general reserving and there was nothing discussed with regards to insurance pricing and underwriting as well.

[27] carried out a study on the Insurance Claim Analysis Using Machine Learning Algorithms. In his study, the author appreciated the role and application of deep learning methods towards claim modeling.

The following descriptions navigate the development of the intended model in the study.

We set up the mentioned eight deep learning methods and within each method we first fitted three types of regression models respectively the Automated Actuarial Loss Reserving Frequency model with dependent variable: Comprehensive Number of Claims (Number of car insurance claims + Number of Requests) being the first, the second being Automated Actuarial Loss Reserving Severity Model with dependent variable: Comprehensive Claim Amount (Claims Incurred + Amount Requested) and lastly Automated Actuarial Loss Reserving Inflation model (Dependent variable: Inflation Index derived from the Consumer Price Index). After fitting these regressions simultaneously, we computed the predictions for each regression type and automated them to give the Inflation Adjusted Automated Actuarial Loss Reserves. From there we calculated the total Inflation Adjusted Automated Actuarial Risk Reserves for each machine learning method.

From there we used the predictions made on the test data set to derive another data set comprising of the Comprehensive Claim Amount from the original test data, Inflation Adjusted AALR which now referred to as Automated Actuarial Loss Reserve Margin (AALRM). With these two variables, we calculated the Upper Automated Actuarial Loss Reserve Margin (UAALRM) by taking the sum of the two variables above and on the same note we obtained the Lower Automated Actuarial Loss Reserve Margin (LAALRM) by subtracting the Automated Actuarial Loss Reserve Margin (AALRM) from Comprehensive claim amount. Finally we obtained the Robust Automated Actuarial Loss Reserve Margin (RAALRM) by taking the average of Upper Automated Actuarial Loss Reserve Margin (UAALRM) and Lower Automated Actuarial Risk Margin (UAALRM). Using these three new variables we created a new reserve data set and partitioned into new train data set (80%) and new test data set (20%). Just after that, we fitted the final regression model for each machine learning model with Robust Automated Actuarial Loss Reserve Margin (UAALRM) as the dependant variable with other two variables which are the Upper Automated Actuarial Loss Reserve Margin (UAALRM) and Lower Automated Actuarial Loss Reserve Margin (LAALRM) as the independent variables. As a result, we derived this as the Final Automated Actuarial Loss Reserving Model (FAALRM) which we used to both estimate and make predictions on Robust Automated Actuarial Loss Reserve Margin (UAALRM). This can now be referred to as Automated Actuarial Loss Reserves (AALR).

We simultaneously fitted three regression models just as in the first stage respectively with the first model being the Automated Actuarial Pricing Frequency model with dependent variable: Comprehensive Number of Payments (Number of Investments + Number of Premium Payments), then the second regression model is the Automated Actuarial Pricing Severity Model with dependent variable: Comprehensive Payment Amount (Claims Paid + Microfinance Amount Paid) and the third regression model is the Automated Actuarial Pricing Inflation model with the dependent variable: Inflation Index derived as well from the Consumer Price Index (CPI). After fitting these regressions simultaneously, we computed the predictions for each regression type and automated them to give the Inflation Adjusted Automated Actuarial Risk Premiums. Afterwards we calculated the total Inflation Adjusted Automated Actuarial Risk Premiums for each machine learning method.

From there we used the predictions made on the test data set to derive another data set comprising of the Comprehensive Payment Amount, Inflation Adjusted Automated Actuarial Risk Premiums which we can now refer to as Automated Actuarial Risk Premium Margin (AARPM). With these two variables we calculated the Upper Automated Actuarial Risk Premium Margin (UAARPM) by taking the sum of the two variables, on the same note we obtained the Lower Automated Actuarial Risk Premium Margin (LAARPM) by subtracting the Automated Actuarial Risk Premium Margin (AARPM) from the Comprehensive Payment amount and finally we obtained the Robust Automated Actuarial Risk Premium Margin (RAARPM) by taking the average of Upper Automated Actuarial Risk Premium Margin (UAARPM) and Lower Automated Actuarial Risk Premium Margin (LAARPM). Using these three main variables we created a new premium data set and partitioned it into new train data set (80%) and new test data set (20%).

Afterwards, we fitted the final regression model for each machine learning model with Robust Automated Actuarial Risk Premium Margin (RAARPM) as the dependent variable whilst the two other variables respectively the Upper Automated Actuarial Risk Premium Margin (UAARPM) and Lower Automated Actuarial Risk Premium Margin (LAARPM) being the independent variables. As a result we hence derived this as the Final Automated Actuarial Risk Premium Model (FAARPM). We then proceed to use this model to both estimate and make predictions on Robust Automated Actuarial Risk Premium Margin (UAARPM) which we can now refer to as Automated Actuarial Risk Premium (AARP).

We created and proposed new terminology concerning actuarial pricing respectively:

• IBNYPP (Incurred But Not Yet Paid Premium)—This refers to the premium that has been incurred by the policyholder but has not yet been paid to the insurer provided that the premiums are not fixed for both car insurance services and micro finance services since they depend on their frequency and severity of premium payments.

• PBNYSPP (Paid But Not Yet Settled Premium Payment)—These refer to the premiums partly paid to the insurance company but not yet fully settled in full, given that the premiums paid by policyholders in their categories vary according to the policyholder’s frequency and severity of premium payments.

• REOPP (Reopened Premium Payment)—These refer to the premiums that were once paid continuously and suddenly stopped due to both certain and uncertain reasons. Now the new streams of premium payments to be rejuvenated by the existing or new policyholder with regards to the same policy are placed in this category.

• REINSPP (Re insured Premium Payment)—This refers to the long overdue, incredibly large unpaid premium which needs to be settled off either by the existing or new policyholder using reinsurance arrangement either internally (with the insurer) or externally (with any other third party of interest).

We also conscripted the existing two main types of actuarial loss reserves in the literature respectively IBNYR and RBNYS. We also introduced two further types of actuarial loss reserves respectively the REOPENED (Reopened Reserve) and the REINSURANCE (Reinsurance Reserve). In short let us define all the adopted and new types of reserves in the context of our automated model for car insurance services and micro finance services as follows.

• IBNYR (Incurred But Not Yet Reported)—these refer to the reserve allocated by the insurer to cater for Incurred claims which are not yet reported or known to the insurance company. These are considered for all the four main policyholder categories defined on Table 2 .

• RBNYS (Reported But Not Yet Settled)—These refer to the reserves allocated by the insurer to cater for Reported But Not Yet Settled claims both from the micro finance services or car insurance services and both.

• REOPENED (Reopened Reserve)—These are actuarial reserves set aside to cater for reported claims that were once closed without payments or with partial payments for both known and unknown reasons, but have been reopened in future date and the insurer needs to meet these long standing claims whether from micro finance services or car insurance services or even both.

• REINSURANCE (Reinsurance Reserve)—These refer to the reserves allocated by the insurer to cater for catastrophic loss reserving either from from micro finance services or car insurance services or even both.

The terminology for Automated Actuarial Loss Reserving Model as well as Automated Risk Pricing Models have been recorded on Table 1 below.

The following Policyholder categories have been suggested towards automation of car insurance services and micro finance services respectively.

Since we are automating car insurance services and microfinance banking services we have considered the four types of policyholder categories defined below.

Table 2 shows the policyholder categories and their associated definitions.

The defined types of actuarial reserves and premiums are then distributed according to the portions shown below.

Table 3 shows the distribution of Total AARR (over the defined types of loss reserves) and also the distribution of Total AARP (over the defined types of risk premiums). From the table above each type of loss reserve has its corresponding type of risk premium as also shown by Table 1 .

Results of Table 4 below shows the Policyholder Loss reserving/premium categories and their associated proportion assumed.

Table 4 shows that category A has large outlay with regards to both types of loss reserves and types of risk premiums respectively followed by Category B, then Category C and lastly Category D which is the reference policyholder category.

Table 5 below shows the types of loading and the associated actuary’s estimated loadings these are used for the Automated Actuarial Risk Premium Pricing.

The pricing loadings are multiplied together with each loading added to 1 in order to give the total premium loadings product which is further multiplied to the estimated AARP. On the same note we do nothing on AARR since the loadings are only for actuarial risk premium pricing.

Using all the assumptions stated in Table 3 and Table 4 above we compute the stated types of risk reserves and premiums respectively using the machine learning algorithms considered in this study. From there the autonomous argumentation of Loss Reserving and actuarial premium pricing commences and proceeds as shown by the next stage below.

Let us consider the framework below between types of loss reserves and risk premiums which is the foundation for Automated Actuarial Loss Reserving & Pricing model.

Table 3 is the building block towards the simultaneous computation of total risk premiums and loss reserves and results are presented in Appendix and see Table A2 . The results shown on this table have been arrived at by taking note of subsection 5 under Table 6 .

At this stage the results from Table A2 is further allocated among the four main types of loss reserves and risk premiums using the Automated Actuarial Loss Reserving and Pricing Assumptions presented on Table 4 . Referring to the Appendix section, we obtain further results respectively; the Automated Actuarial Loss Reserving & Pricing Total IBNYR Reserves and IBNYPP Premiums shown from Table A3 , Automated Actuarial Loss Reserving & Pricing Total RBNYS Reserves and PBNYSP Premiums from Table A4 , Automated Actuarial Loss Reserving & Pricing Total ROPENED Reserves and REOPP Premiums from Table A5 and finally the Automated Actuarial Loss Reserving & Pricing Total REINSURANCE Reserves and REINSPP Premiums from Table A6 .

Here we sum the above calculated allocated Automated Actuarial Loss Reserving & Pricing Balances between Policyholder Categories from Subsection 6 above and obtain the Comprehensive Automated Actuarial Loss Reserving & Pricing Total Reserves and Premiums shown in the Appendix Section under Table A7 .

At this stage we then proceed to sum the Comprehensive Automated Actuarial Loss Reserving & Pricing Balances determined from Subsection 6 above and hence we arrived at Aggregate Comprehensive Automated Actuarial Loss Reserving & Pricing Total Reserves and Premiums as reflected by Table A8 .

Ultimately, we then use the policyholder Category No Claims Bonus rates in order to find the net present values and accumulated values for Aggregate Comprehensive Automated Actuarial Loss Reserving & Pricing Total Reserves and Premiums among the policyholder categories from Table A8 . These bonus rates are used to navigate Automated Actuarial Underwriting modeling respectively.

Our model is an automation of car insurance services and micro finance services on the same platform with the aim to reducing the comprehensive number of claims by targeting reducing the number of claims (from Policyholders in categories A and B) and number of requests (from Policyholders in categories A and C) whilst simultaneously promoting increase in comprehensive number of payments to the insurere in form of increasing number of premium payments once the premium is due (from Policyholders in categories A and B) and also increasing the number of investments (from Policyholders in categories A and C). As a result, Table 7 shows No Claims bonus rates for all policyholders in their diverse categories. It is quite interesting that during the Automated Actuarial Underwriting (AAU) modeling the base bonus rates are given to all policyholders as soon as they take any policy (A, B and C) from the insurer, also on the same platform the variable bonus rate is added on to the base bonus rate until we arrive at the final bonus rate. According to our model the more the policyholder claims the variable bonus rate falls and the lesser the number of claims the better the variable bonus rate. From Table 7 Policyholder category A has the largest maximum final bonus rate (5%) followed by Policyholder category B’s maximum final bonus rate (4%), then Policyholder category C’s maximum final bonus rate (3%) and the least being Policyholder category D’s maximum final bonus rate (0%) since this category has no participant/active policyholders. In a nutshell these rates are applied on the derived Automated Actuarial Loss Reserving & Pricing Balances (AALRPB) for all policyholders in their respective categories taken from Table 6 .

The following steps are considered in order to develop the Automated Actuarial Underwriting model.

The major source of our expenses came from initial expenses, renewal expenses, taxes paid, underwriting costs and fees paid whilst our major source of income came from retained earnings. These incomes and expenses were totaled with respect from each mentioned category in the new test data set to match with the final regression estimating Automated Actuarial Loss Reserving & Pricing (AALRP) models Table 19 . Soon afterwards we totaled all expenses to get the aggregate total for all the expenses and then distributed them between the policyholder categories A (50%), B (30%), C (20%) and D (0%) see Table 4 . This enabled us to set up the actuarial underwriting model with respect to each category and also to maintain effectiveness, efficiency and economic distribution of expenses and outgo.

The following method was used for determining the prevailing interest rates respectively. We then simulated prevailing interest rates in R using uniform distribution. We assumed a period of 100 years which we took as n, in addition to that we considered the prevailing annual interest rates to vary between minimum (1%) and maximum (5%). We then computed the average for the simulated prevailing annual interest rates which came to (3.05%). This is the final interest rate which we considered for determining the net present value for evaluation of net AALRPB of expenses and outgo respectively presented by Table 8 below.

The Automated Actuarial Underwriting model is carried out within each Policyholder category starting with A, B and ending with C. The AAU model proceeds from the AALRP model balances, moreover AAU is evaluated in the following five stages by taking the first 100 years as the longest possible underwriting. Moreover, on the same note, we considered the same model for the first ten years which we proposed to the shortest possible time towards effective model testing towards the proposed actuarial underwriting method suggested in this study. Note that FBR is the Final Bonus Rate and E_t represents the Expenses and outgo at time t.

${\left(\text{AAU}\right)}_t=(\begin{array}{ll}{\displaystyle \sum }\left({\text{AALRPB}}_t\cdot {\left(1+\text{FBR}\right)}^t-E_t\right)v^t>0\hfill & \text{AAU}\text{is}\text{possible}\hfill \\ {\displaystyle \sum }\left({\text{AALRPB}}_t\cdot {\left(1+\text{FBR}\right)}^t-E_t\right)v^t<0\hfill & \text{Go}\text{to}\text{next}\text{stage}\hfill \end{array}$(13)

where $AALRP{B}_t={\left(IBNYR+IBNYPP\right)}_t$ and $V^t={\left(1+\text{average}\text{simulated}\text{annual}\text{prevailing}\text{rate}\right)}^{-t}$.

${\left(\text{AAU}\right)}_t=(\begin{array}{ll}{\displaystyle \sum }\left({\text{AALRPB}}_t\cdot {\left(1+\text{FBR}\right)}^t-E_t\right)v^t>0\hfill & \text{AAU}\text{is}\text{possible}\hfill \\ {\displaystyle \sum }\left({\text{AALRPB}}_t\cdot {\left(1+\text{FBR}\right)}^t-E_t\right)v^t<0\hfill & \text{Go}\text{to}\text{next}\text{stage}\hfill \end{array}$(14)

where $AALRP{B}_t={\left(IBNYR+IBNYPP\right)}_t+{\left(RBNYS+PBNYSPP\right)}_t$.

${\left(\text{AAU}\right)}_t=(\begin{array}{ll}{\displaystyle \sum }\left({\text{AALRPB}}_t\cdot {\left(1+\text{FBR}\right)}^t-E_t\right)v^t>0\hfill & \text{AAU}\text{is}\text{possible}\hfill \\ {\displaystyle \sum }\left({\text{AALRPB}}_t\cdot {\left(1+\text{FBR}\right)}^t-E_t\right)v^t<0\hfill & \text{Go}\text{to}\text{next}\text{stage}\hfill \end{array}$(15)

where $\begin{array}{c}AALRP{B}_t={\left(IBNYR+IBNYPP\right)}_t+{\left(RBNYS+PBNYSPP\right)}_t\\ +{\left(REOPENED+REOPP\right)}_t\end{array}$.

${\left(\text{AAU}\right)}_t=(\begin{array}{ll}{\displaystyle \sum }\left({\text{AALRPB}}_t\cdot {\left(1+\text{FBR}\right)}^t-E_t\right)v^t>0\hfill & \text{AAU}\text{is}\text{possible}\hfill \\ {\displaystyle \sum }\left({\text{AALRPB}}_t\cdot {\left(1+\text{FBR}\right)}^t-E_t\right)v^t<0\hfill & \text{Go}\text{to}\text{next}\text{stage}\hfill \end{array}$(16)

where $\begin{array}{c}AALRP{B}_t={\left(IBNYR+IBNYPP\right)}_t+{\left(RBNYS+PBNYSPP\right)}_t\\ +{\left(REOPENED+REOPP\right)}_t+{\left(REINSURANCE+REINSPP\right)}_t\end{array}$.

${\left(\text{AAU}\right)}_t={\displaystyle \sum }\left({\text{AALRPB}}_t\cdot {\left(1+\text{FBR}\right)}^t-E_t\right)v^t>0\text{AAU}\text{is}\text{possible}$(17)

where $\begin{array}{c}{\text{AALRPB}}_t={\left(\text{IBNYR}+\text{IBNYPP}\right)}_t+{\left(\text{RBNYS}+\text{PBNYSPP}\right)}_t\\ +{\left(\text{REOPENED}+\text{REOPP}\right)}_t+{\left(\text{REINSURANCE}+\text{REINSPP}\right)}_t\\ +\text{TOTAL}\text{RETAINED}{\text{INCOME}}_t\end{array}$.

The proposed methodology in this study introduces several novel concepts and builds upon existing machine learning techniques: Introducing terms such as IBNYPP (Incurred But Not Yet Paid Premium) and PBNYSPP (Paid But Not Yet Settled Premium Payment) to better categorize and manage different types of premiums. The study integrates new types of reserves like REOPENED and REINSURANCE reserves into the actuarial framework, expanding the traditional categories to better capture long-standing and catastrophic risks. The multi-stage Automated Actuarial Underwriting (AAU) model evaluates underwriting feasibility over multiple stages, considering various reserve and premium categories for more precise decision-making. The incorporation of an inflation-adjusted model accounts for economic changes, enhancing the accuracy of predictions over time. This methodology not only leverages the strengths of machine learning algorithms but also introduces a structured framework that comprehensively addresses the complexities of modern insurance practices.

The following are defined principal data variables and how they have been derived.

• Comprehensive Claim Amount = (Claims Incurred + Amount Requested)—where Claim Incurred comes from car insurance services and Amount Requested comes from microfinance services.

• Comprehensive Number of Claims = (Number of Claims + Number of Requests)—where Number of Claims comes from car insurance services and Number of Requests comes from microfinance services.

• Comprehensive Payment Amount = (Current Premium + Amount Invested)—where the Current Premium comes from car insurance service policyholders and Amount Invested comes from microfinance services policyholders.

• Comprehensive Number of Payments = (Number of Investments + Number of Premium Payments)—where both the Number of Investments and Number of Requests come from policyholders affiliated to both or either car insurance services or microfinance services.

Further exploratory results for the key principal variables are shown in Figures 1-4 below.

Figures 1-4 reveal that the box in each plot represents the interquartile range (IQR), which contains the middle 50% of the data. The bottom and top edges of the box represent the first quartile (Q1) and third quartile (Q3) respectively. The length of the box (height in vertical box plots) indicates the spread of the middle 50% of the data. The line inside the box represents the median value of the data. It shows the central tendency of the distribution. The whiskers extend from the edges of the box to the smallest and largest observations within 1.5 times the IQR from the edges of the box. They indicate the range of the data, excluding potential outliers. Individual points beyond the whiskers represent potential outliers—data points that are significantly different from the rest of the data. Outliers may suggest unusual or extreme values in the simulated data set.

Correlation analysis is a statistical technique used to measure the strength and direction of the relationship between two or more variables. It quantifies the degree to which changes in one variable are associated with changes in another variable [28] . The result of correlation analysis is a correlation coefficient ρ, which indicates the strength and direction of the relationship between variables. The ρ typically ranges between −1 and 1. Furthermore, correlation coefficient of 1 indicates a perfect positive correlation, meaning that as one variable increases, the other variable also increases proportionally. A ρ of −1 indicates a perfect negative correlation, meaning that as one variable increases, the other variable decreases proportionally. A ρ of 0 indicates no correlation between the variables. There are different methods to calculate correlation coefficients, including Pearson correlation coefficient (for linear relationships), Spearman ρ (for monotonic relationships), and Kendall correlation coefficient (for ordinal relationships) [29] . The choice of method depends on the nature of the data and the relationship being investigated.

Figure 5 shows that there is perfect correlation among the principal data variables themselves as shown by the red colored box with value of (1.00). On the same note the correlation between the other variables is nearly 0.00 which shows that there is independence and absolutely no dependency among the other variables. This clearly shows that the claims and payment characteristics of policyholders in their diverse categories are very random. As a result of this, there is need for insurance company to set aside readily available large stake of Automated Actuarial Loss Reserving Risk Pricing Balances (AALRRPB) to cater for uncertain claims which this study has provided an alternative solution to this problem. This is also validated by the correlation matrix presented on Table 9 .

Factor Analysis (FA) and Principal Component Analysis (PCA) are both multivariate statistical techniques used for data reduction and dimensionality reduction [30] . Factor Analysis is a statistical method used to identify underlying factors or latent variables that explain the correlations among observed variables. In addition to that, the primary goal of FA is to uncover the structure of relationships between observed variables and to understand the underlying constructs or factors that are responsible for these relationships.

FA assumes that observed variables are linear combinations of unobserved (latent) factors plus error terms. It seeks to explain the covariance between variables in terms of a smaller number of latent factors. Furthermore, FA allows for the interpretation of the data in terms of underlying constructs and can be used for data reduction and simplification. Factor loadings represent the correlations between observed variables and underlying factors, and they indicate how much each variable contributes to each factor.

Principal Component Analysis is a technique used to transform a set of correlated variables into a set of uncorrelated variables called principal components [31] . The primary goal of PCA is to reduce the dimensionality of the data while preserving as much of the variability in the data as possible. PCA achieves dimensionality reduction by identifying a set of orthogonal axes (principal components) that capture the maximum variance in the data. Unlike Factor Analysis, PCA does not assume the presence of latent factors underlying the observed variables. Instead, it focuses on finding linear combinations of variables that explain the most variance in the data.

Moreover, PCA does not provide direct interpretation of underlying constructs or factors. Instead, it provides a data-driven representation of the structure of the data based on variance [32] . Principal components are ordered in terms of the amount of variance they explain, with the first component explaining the most variance and subsequent components explaining decreasing amounts of variance.

In short, while both FA and PCA are used for data reduction and dimensionality reduction, Factor Analysis focuses on uncovering underlying constructs or factors that explain correlations between observed variables, while PCA focuses on capturing the maximum variance in the data through orthogonal transformations of the variables. The choice between FA and PCA depends on the research question, assumptions about the data, and the objectives of the analysis [32] .

Figure 6 below shows the importance of these key variables in our study.

From Figure 6 , there is evidence of the presence of unit root which suggests both weak and strong negative and positive influence of each key variable in the study. As a result these variables have been used to develop the Automated Actuarial Pricing and Underwriting Model respectively presented by the Table 10 below.

The eigenvalues are all positive and greater than 1 which suggests that the four variables are very important in the study, see Table 11 below.

The standardized loadings, often found in factor analysis, represent the correlations between observed variables (indicators) and latent factors, which are standardized to have a mean of zero and a standard deviation of one. These loadings indicate the strength and direction of the relationship between each observed variable and the underlying factor (s) being measured. The absolute value of the loading indicates the strength of the relationship between the variable and the factor. Higher absolute values (closer to 1) suggest a stronger relationship and this is presented by Comprehensive Number of Claims and Comprehensive Number of Payments. A positive loading indicates a positive correlation between the variable and the factor, meaning that as the variable increases, so does the underlying factor. Conversely, a negative loading indicates an inverse relationship: as the variable increases, the factor decreases.

In factor analysis, “SS Loadings” stands for “Sum of Squared Loadings.” It is a metric that represents the proportion of variance in the observed variables (indicators) that is accounted for by each latent factor. SS Loadings are calculated by summing the squares of the factor loadings for each variable on a specific factor. Proportion of Variance Explained: SS Loadings provide insight into how much of the total variance in each observed variable is explained by the underlying factors. In addition to that, we have higher SS Loadings indicate that a larger proportion of the variance in the variable is captured by the factor. Table 12 indicates positive and large proportion variance and Cumulative Variance which ultimately leads to large Proportion Explained and Cumulative Proportion a clear indication that the four factors are important in the model. In short, the SS Loadings can be used as indicators of the goodness-of-fit of the factor model. The higher SS Loadings displayed suggest a better fit, as they indicate that the factors are accounting for a larger proportion of the variance in the data.

After loading the data in R, we both hot encored the data using R caret package and preprocessed it using the min-max approach before partitioning it into training data set (80%) and test data set (20%).

The Automated Actuarial Loss Reserving Risk Pricing Frequency models are presented below.

Table 13 shows that SVM took affectionately long time to process the results for both Automated Loss Reserving and Automated Actuarial Risk Pricing frequency models. On the same spot both GLM, GAM and ANN converged faster for both models. In addition to that, Regression Trees (RPART), Random Forests (RANGER), XGB and LAR took much longer to process both the frequency models. All the machine learning models used to construct both types of models gave almost the same values with regards to model evaluation and performance metrics which are MSE, MAE and RMSE and this reflects both the reliability and validity of machine learning models.

The Automated Actuarial Loss Reserving Risk Pricing Severity Models are presented below.

Table 14 reveals that the SVM machine learning model respectively took much longer time to give results for both Automated Loss Reserving Severity and Automated Risk Pricing Severity models. On the same note, GLM and GAM were the most fastest models that gave the results in the shortest possible time looking at both severity models. On the same note, Regression Trees (RPART), Random Forests (RANGER), XGB and LAR took much longer to process both severity models. From Table 10 , all the machine learning models gave almost the same values for the machine learning model evaluation and performance metrics which indicates the reliability and validity of machine learning models.

This model is aimed at both adjusting and stabilizing the frequency-severity models above with the zeal of coming up with inflation adjusted automated actuarial loss reserves risk premiums balances accordingly. Since we appreciate that the higher the rate of inflation the faster the rate of comprehensive claims as compared to comprehensive payments and the reverse being true [33] , we considered running the two inflation models one for adjusting and stabilizing the Automated Actuarial Loss Reserving frequency and severity models and also the other doing the same task with respect to Automated Actuarial Risk Pricing frequency and severity models as shown below.

Table 15 shows that SVM was the slowest model to give the results for inflation adjusted frequency severity models for both models. This is well exhibited by their exceptionally large processing time compared to GLM, GAM, RPART and ANN whose processing time is quite faster. On the same note, RANGER and LAR took much longer processing time with respect to the two presented models. Table 11 also shows that all the eight machine learning models gave approximately quite similar results for performance metrics which absolutely displays reliability and validity of results.

Total Automated Actuarial Inflation Adjusted Loss Reserves and Risk Premiums is computed for each machine learning algorithm as shown below. The results are shown on Table 16 .

Table 16 shows that the Total Automated Actuarial Inflation Adjusted Risk Reserves and Premiums predictions are approximately close to each other since their model performance metrics revealed that they were also similar to each other.

Using the approach explained in our methodology sections subsection 0.0.4 and 0.0.5 we obtained the following final model for Automated Actuarial Loss Reserving Risk Pricing model.

Table 17 shows that RANGER, LAR, XGB and ANN algorithms took the high processing time across the two final automated models for Automated Actuarial Loss Reserving (AALR) and Automated Actuarial Risk Pricing (AARP). Moreover, the similar results obtained for predicted values for AALR and AARP reveal homogeneity, consistency, stability and reliability of results.

Figure 7 below shows how the Automated Actuarial Loss Reserves Risk Pricing Balances (ALRRPB): Total Reserves and Total Premiums have been distributed among the types of loss reserves and also types of risk premiums, see the methodology subsection 6, as a result, the tables of results presented in the Appendix section shows the outcome, see Table A2 with loss reserve-risk premium allocations taken from Table 3 .

Figure 7 shows the AALRRPB (Total Reserves + Total Premiums) derived from the Automated Actuarial Loss Reserves and Automated Actuarial Risk Premiums predicted from their final models as respectively shown on Table 13 . From Figure 7 RANGER scooped the largest stake for AALRRPB respectively.

Figures 8-11 below shows the allocated the Total Automated Actuarial Loss Reserves Risk Pricing Balances distributed across policyholder loss reserving-risk premium categories.

Figures 8-11 above show that the RANGER algorithm recorded a large stake of AALRRPB (IBNYR + IBNYPP), AALRRPB (RBNYS + PBNYSPP), AALRRPB (REOPENED + REOPP) and also AALRRPB (REINSURANCE + REINSPP). Across all the policyholder categories the AALRRPB (IBNYR + IBNYPP) enjoyed the largest portion, followed by AALRRPB (RBNYS + PBNYSPP), then AALRRPB (REOPENED + REOPP) and finally the AALRRPB (REINSURANCE + REINSPP) being the least. From Figures 8-11 , it is clear that Policyholder category A enjoyed the largest portion of four main types of reserves and risk premiums followed by Category B, then Category C and lastly Category D. Nevertheless, Category D has attained (0%) across all the types of loss reserves and risk premiums, since there are no any active policyholders as also presented on Table 4 . In reference to Figures 8-11 large quantities of AALRRPB have been allocated to (IBNYR + IBNYPP) layer since it caters most for unreported comprehensive claims coming from both the microfinance policyholders and car insurance policyholders, as a result Category A which consists of policyholders with both policies has been allocated a larger portion. Consequently, the presence of other premium-reserve portions such as AALRRPB (RBNYS + PBNYSPP), AALRRPB (REOPENED + REOPP) and AALRRPB (REINSURANCE + REINSPP) in all policyholder categories reduces the reinsurance layers and costs to minimum levels if not zero, whilst promoting catastrophic reserving and comprehensive claim settlements in the shortest possible time with very minimum if at most zero reporting and settlement delays.

The CAALRRPB have been obtained by summing the Comprehensive Automated Actuarial Loss Reserves (CAALR) and Comprehensive Automated Actuarial Risk Premiums (CAARP) as directed under methodology sub subsection 6 and results are also presented on the Appendix section, see Table A7 whose results are shown by Figure 12 .

Since Category A carries the largest stake on allocation and Figure 12 . Comprehensive Automated Actuarial Loss Reserves Risk Pricing Balances distribution of reserves, see Table 4 followed by Category B, then Category C and eventually Category D the reference. Clearly from Figure 12 , RANGER recorded the highest value for AALRRPB (CAALR + CAARP) respectively.

This is obtained by summing the calculated CAALRRPB with regards to methodology Subsection 6. Table 7 shows the results which then are produced in Figure 13 .

From Figure 13 , the ACAALRRPB for RANGER recorded the highest peak which apparently makes it the best model for Automated Actuarial Underwriting process. This is so because by having large stake of ACAALRRPB set aside that means the insurance company has the largest outlay of funds in form of ACAALRRPBs set aside for uncertain comprehensive claims from the main three policyholder categories defined in this study. This also prepares the insurer for large loss reserving respectively the catastrophic loss reserving as well as risk premium pricing.

This section commences the journey towards Automated Actuarial Underwriting with regards to Table 18 below.

Table 18 shows evidence of positive surplus of (1,188,879,624.44) coming from retained earnings. This is a positive sign for cash generative business, it also reflects profitability and better liquidity levels since the total Retained income is able to cover all the expenses and outgo in this case. Moreover, the positive and large value for the surplus is a clear sign that there is credible business expansion as a result of automation of car insurance services and microfinance services simultaneously. On the same note high value for the surplus indicates more influx of income from comprehensive payments inform of investments and premium payments while on the same note there is credible evidence of decreasing comprehensive claims coming from car insurance policy claims and amount of money requested by policyholders in their diverse categories as indicated by recorded zero values for Total Claims incurred and Total Claims Outstanding. This is facilitated, by the fact that the policyholders in their categories seek to keep the frequency and severity of claims lower so that they benefit from a better rate of return on their stake credited with the maximum final bonus rate.

Table 19 shows the distribution of total expenses according to the proposed allocations presented on Table 4 . The total expenses and outgo of (11,203,278.56) were distributed according to their allocation shown in Table 19 . As a matter of consequence, the Category A carries the largest figure for total expenses and outgo with (5,601,639.28), followed by Category B with total expenses and outgo totaling (3,360,983.57), Category C’s total expenses and outgo comes to a figure of (2,240,655.71). Moreover Category D, had zero expenses and outgo since it is the reference category without any participant policyholder. These values of total expenses and outgo recorded by each policyholder category are employed towards the Automated Actuarial Underwriting modeling process with regards to each category.

This section shows results for the Automated Actuarial Underwriting from Automated Actuarial Loss Reserving Risk Pricing models and the following assumptions were used to develop the following models.

• The moment a policyholder takes the policy he/she receives the base bonus rates shown on Table 7 .

• The AALRRPB are compounded over n period of time to forecast their respective accumulated value using final bonus rates.

• n can be number of days, number of weeks, number of months and or number of years.

• The number of comprehensive payments is greater than the number of comprehensive claims.

• Expenses and outgo are deducted from the accumulated AALRRPB and the net balance is evaluated at prevailing rates shown on Table 8 .

• The frequency, Severity and inflation rates are constant over n.

• The expenses and outgo are constant over n.

• Random Forest (RANGER) being the best model machine learning model in the study has been used to develop the final Automated Actuarial Underwriting Model, see Figure 13 .

• Automated Actuarial Underwriting model is carried out for categories A, B and C only since D is the reference category without any active policyholder.

The Automated Actuarial Underwriting process commences with AAUM Stage 1 0.0.8 followed by AAUM Stage 2 0.0.9, then AAUM Stage 3 0.0.10 and finally AAUM Stage 4 0.0.11. The ACAALRRPB were cumulatively added at each stage and thereafter remaining with net cash flows after taking away the respective expenses and outgo in the corresponding policyholder category, see Table 19 . The net present value is then computed for the net cash flow balances using the prevailing interest rate shown on Table 8 .

We tested our model with n = 100 years which is essentially the longest possible time the insurance company operating with the assumptions discussed above applying and hence the Automated Actuarial Underwriting results are shown below.

Table 20 above shows the results for Automated Actuarial Underwriting models for Policyholder Category A, Policyholder Category B and Policyholder Category C. From these three models each model has four stage AAU process the first being stage 1 AAU see the equation 13, second Stage 2 AAU see equation 14, third Stage 3 AAU see equation 15, fourth Stage 4 AAU see equation 16 and finally Stage 5 AAU see equation 17. There is no fifth stage in the above models since all the total expenses distributed in the respective presented policyholder categories have been underwritten from stage 1 leaving off a large chunk of positive and large net AALRRPB cash flow balances and hence bringing us to the fact that in all these stages Automated Actuarial Underwriting of all claims, expenses and outgo has been quite effective within the first 100 years of implementing this model. Taking a closer look at these three models the quantum of AALRRP balances is greatest in Stages 1, followed by Stage 2, then Stage 3 and finally Stage 4. The presence of large and positive AAU net present values across the three policyholder categories shows that a large chunk of ACAALRRPB have been spared for future growth and catastrophic reserving and thus reducing both the incidence, prevalence as well as the severity of reinsurance in its diverse forms. Large and positive AAU net present values are due to more comprehensive payments being made and reduced frequency and severity of comprehensive claims. This is a clear indication of cash generative and profitability business and hence this reflects that the insurance company has the capability to boost its financial performance, organizational productivity, reduced solvency margin in line with IFRS17 guidelines. As a result, automation of microfinance and car insurance services steers up the insurer’s profitability and reduces the solvency risk as far as actuarial underwriting is concerned.

We also validated our model by forecasting the net present values for Automated Actuarial Underwriting Model using the earliest possible time, which is the first 10 years, as a matter to test our model and see if the model also works well within this period of time. The results are shown below.

In addition to that, Figures 14-16 display a visual presentation of Automated Actuarial Underwriting for the first 10 years taken from Table 21 . Furthermore, these figures show a positive trend in the predicted NPV Automated Actuarial Underwriting.

Balances that indicate growth in the net ACAALRRPB cash flows after the underwriting of all expenses and outgo. Our proposed Automated Actuarial Underwriting model in four stages has immediately given large positive quantum of net AAU from the negative NPVs for AAU in Years 1 and 2 across the three policyholder categories. This has been possible just at AAU Stage 2 leaving off other stages with enormous amounts of money which the insurance company can readily plough back into its future projects.

As a result, our model works well in both scenarios such as the longest possible time where n = 100 years and the earliest possible time where we validated our model with the first 10 years of operation. In both scenarios our model works well since there are large sums of net AAU model balances set aside for the future use by the insurance company.

This section shows the remarks concerning our study.

Full implementation of our model mitigates and reduces the riskiness of failure by an insurance company since the various types of risks such as liquidity risks, currency risks, group risks just to mention a few are most likely to be reduced greatly. For example, the large and positive net AAU cash flows cash generated from the automated microfinance and car insurance services help a lot to diminish the liquidity risk. Moreover, these net large and positive AAU cash flows are then channeled towards underwriting of comprehensive claims, expenses and related outgo [34] - [36] .

Our model does support all the accounting concepts such as the money measurement concept, going concern concept, realization concept, prudence concept and accruals concept just to mention a few. The simultaneous and autonomous automation of microfinance services and car insurance services using Artificial Intelligence based methods ensures that the insurance 17 and 16. In a similar fashion our study conforms to IFRS17 standards [37] and [38] .

Asset-liability management attempts to find the optimal investment strategy under uncertainty in both the asset and liability streams. The developed Automated Actuarial Pricing and Underwriting Model results in more comprehensive payments in form of amounts of money invested and the current premiums (thus boosting and increasing the asset base of the insurer) paid whilst decreasing the comprehensive claims, expenses and outgo (reducing the liability base of the insurer) [39] - [42] .

Our model does not require the use of broker and other related insurance intermediaries since it deals directly with the policyholders in their respective categories and hence the broking costs are brought to zero. Furthermore, the policyholder is capable of knowing his/her premiums and also the amounts of money invested and requested from the AI-based model. Eventually, this reflects effectiveness and efficiency of our model [43] - [45] .

The setting up of the AALRRPB (IBNYR + IBNYPP): see Table A3 , AALRRPB (RBNYS + PBNYPP): see Table A4 , AALRRPB (REOPENED + REOPP): see Table A5 and AALRRPB (REINSURANCE + REINSPP): see Table A6 is meant to reduce drastically all forms of reinsurance by the insurer which are facultative reinsurance, excess of loss reinsurance, proportional reinsurance and catastrophic reinsurance. The augmentation of microfinance services and car insurance services on the same platform using Artificial Intelligence is a substantive step towards generating and guaranteeing large pool of funds to the insurer and thus reducing the quantum of reinsurance almost to zero since the insurance company is then capable of underwriting all its future claims with minimum or no reinsurance [46] and [47] .

The presence of the no-claims bonus rate system (see Table 7 ) across all the possible policyholder categories is a step towards these policyholders in their respective categories to reduce both the severity and frequency of comprehensive claims. Such a step turns to bring down the Underwriting expenses and outgo as one wishes to maximize his/her final bonus rate in order to earn a greater return [48] - [50] .