Journal article

The expected discounted penalty function: from infinite time to finite time

S Li, Y Lu, KP Sendova

Scandinavian Actuarial Journal | Taylor & Francis (Routledge) | Published : 2019

Abstract

In this paper we study the finite-time expected discounted penalty function (EDPF) and its decomposition in the classical risk model perturbed by diffusion. We first give the solution to a class of second-order partial integro-differential equations (PIDEs) with certain boundary conditions. We then show that the finite-time EDPFs as well as their decompositions satisfy this specific class of PIDEs so that their explicit expressions are obtained. Furthermore, we demonstrate that the finite-time EDPF may be expressed in terms of its ordinary counterpart (infinite-time) under the same risk model. Especially, the finite-time ruin probability due to oscillations and the finite-time ruin probabili..

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University of Melbourne Researchers