TITLE:
Ruin Probabilities and Complex Analysis
AUTHORS:
Andrew P. Leung
KEYWORDS:
Reserves, Ruin Probability in Infinite Continuous Time, Lebesgue Spaces, Fourier Transform, Inverse Fourier Transform, Analytic Functions, Cauchy’s Theorem
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.12 No.1,
February
22,
2022
ABSTRACT: This paper considers the solution of the equations for ruin probabilities in infinite continuous time. Using the Fourier Transform and certain results from the theory of complex functions, these solutions are obtained as complex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the results obtained for the continuous time cases, and those in the literature, are compared. Closed form ruin probabilities for the heavy tailed distributions: mixed exponential; Gamma (including Erlang); Lognormal; Weibull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).