The Ruin Probability in a Risk Model with Injections

Title & Authors
The Ruin Probability in a Risk Model with Injections
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 $\small{{\tau}}$(0 < $\small{{\tau}}$ < 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
Cited by
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