The Ruin Probability in a Risk Model with Injections

- Journal title : Korean Journal of Applied Statistics
- Volume 25, Issue 1, 2012, pp.81-87
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2012.25.1.081

Title & Authors

The Ruin Probability in a Risk Model with Injections

Go, Han-Na; Choi, Seung-Kyoung; Lee, Eui-Yong;

Go, Han-Na; Choi, Seung-Kyoung; Lee, Eui-Yong;

Abstract

A continuous time risk model is considered, where the premium rate is constant and the claims form a compound Poisson process. We assume that an injection is made, which is an immediate increase of the surplus up to level u > 0 (initial level), when the level of the surplus goes below (0 < < u). We derive the formula of the ruin probability of the surplus by establishing an integro-differential equation and show that an explicit formula for the ruin probability can be obtained when the amounts of claims independently follow an exponential distribution.

Keywords

Risk model;surplus process;ruin probability;injection;integro-differential equation;

Language

Korean

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