Moments of the time of ruin in a renewal risk model with discounted penalty
Abstract
Purpose
This paper considers a Sparre Andersen risk process for which the claims inter‐arrival distribution is Generalized Exponential. The purpose of this paper is to find explicit expressions for the moments of time to ruin when a penalty is imposed at ruin.
Design/methodology/approach
The study is focused on the function ϕδ(u), the expected discounted penalty, which is due at ruin and may depend on the deficit at the time of ruin and also on the surplus prior to ruin. It shows that ϕδ(u) satisfies an integro‐differential equation which is solved using Laplace transforms.
Findings
The authors have chosen a penalty function, which is independent of the surplus immediately before ruin, and a closed form expression is obtained for ϕδ(u), and then solved for the moments of time to ruin.
Originality/value
New results are derived, many of which have mathematical and probabilistic interpretations, and additional insight is gained for the results in the renewal risk model.
Keywords
Citation
Thampi, K.K. and Jacob, M.J. (2008), "Moments of the time of ruin in a renewal risk model with discounted penalty", Journal of Risk Finance, Vol. 9 No. 2, pp. 173-187. https://doi.org/10.1108/15265940810853922
Publisher
:Emerald Group Publishing Limited
Copyright © 2008, Emerald Group Publishing Limited