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On the surplus prior to ruin in the perturbed classical risk process

Jiandong Ren (Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, Ontario, Canada)

Journal of Risk Finance

ISSN: 1526-5943

Article publication date: 6 March 2007

482

Abstract

Purpose

The purpose of this article is to consider the classical risk model that is perturbed by a Brownian motion process. The article derives explicit formulas for the joint and marginal probability density functions of the surplus prior to ruin and the deficit at ruin.

Design/methodology/approach

This article first extends the dual argument to probabilistically explain the symmetry between the two random variables related to the so‐called modified ladder height. Then the paper uses renewal arguments to derive the joint distribution of the surplus prior to ruin and the deficit at ruin.

Findings

The study derived an explicit formula for the undiscounted joint density in the perturbed risk model that is directly parallel to formula (3.2) for the classical risk model. The formula clearly shows that in a perturbed risk process, when ruin is caused by a claim, the p.d.f. of the surplus prior to ruin is continuous. In addition, shows that when the claim sizes follow a phase‐type distribution, all the relevant quantities can be conveniently computed.

Originality/value

The dual argument used in this article is novel. The formula first clearly shows that in the perturbed risk model, the p.d.f. of the surplus prior to ruin is continuous. When claim sizes are phase‐type, the formulas can be conveniently computed.

Keywords

Citation

Ren, J. (2007), "On the surplus prior to ruin in the perturbed classical risk process", Journal of Risk Finance, Vol. 8 No. 2, pp. 186-195. https://doi.org/10.1108/15265940710732350

Publisher

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Emerald Group Publishing Limited

Copyright © 2007, Emerald Group Publishing Limited

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