TITLE:
On a Compound Poisson Risk Model Perturbed by Brownian Motion with Variable Premium and Tail Dependence between Claims Amounts and Inter-Claim Time
AUTHORS:
Delwendé Abdoul-Kabir Kafando, Kiswendsida Mahamoudou Ouedraogo, Pierre Clovis Nitiema
KEYWORDS:
Gerber-Shiu Function, Copula, Integro-Differential Equation, Laplace Trans-form, Brownian Motion
JOURNAL NAME:
Open Journal of Statistics,
Vol.14 No.1,
February
2,
2024
ABSTRACT: This paper considers the compound Poisson risk model perturbed by Brownian motion with
variable premium and dependence between claims amounts and inter-claim times
via Spearman copula. It is assumed that the insurance company’s portfolio is
governed by two classes of policyholders. On the one hand, the first class
where the amount of claims is high, and on the other hand, the second
class where the amount of claims is low, this difference in claim amounts has
significant implications for the insurance company’s pricing and risk management
strategies. When policyholders are in the first class, they pay an insurance
premium of a constant amount c1 and when they are in the second class, the premium paid is a constant amount c2 such that c1 > c2. The nature of claims (low or high) is
measured via random thresholds . The study in this work will focus on the
determination of the
integro-differential equations satisfied by Gerber-Shiu functions and their
Laplace transforms in the risk model perturbed by Brownian motion with variable
premium and dependence between claims amounts and inter-claim times via
Spearman copula.