Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Ruin Probabilities and Complex Analysis

Version 1 : Received: 15 December 2021 / Approved: 20 December 2021 / Online: 20 December 2021 (09:47:46 CET)

How to cite: Leung, A. Ruin Probabilities and Complex Analysis. Preprints 2021, 2021120298. https://doi.org/10.20944/preprints202112.0298.v1 Leung, A. Ruin Probabilities and Complex Analysis. Preprints 2021, 2021120298. https://doi.org/10.20944/preprints202112.0298.v1

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 com- plex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the re- sults 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; Weillbull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).

Keywords

reserves; ruin probability in infinite continuous time, Lebesgue spaces; Fourier Transform; Inverse Fourier Transform; analytic functions; Cauchy’s Theorem

Subject

Computer Science and Mathematics, Probability and Statistics

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