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April  2006, 2(2): 229-236. doi: 10.3934/jimo.2006.2.229

Ruin probability for renewal risk model with negative risk sums

Yinghui Dong 1, and  Guojing Wang 2,

1. 

Department of Mathematics, Suzhou Technology University, Suzhou 215011, P.R., China
2. 

Department of Mathematics, Suzhou University, Suzhou 215006, P.R., China

Received  December 2005 Revised  January 2006 Published  April 2006

In this paper, we consider a renewal risk process with negative risk sums. We derive integral equations and integro-differential equations for the survival and ruin probabilities for the proposed model. Exact expression and upper and lower bounds for the ruin probability are obtained. We also present some closed form expressions for the survival and ruin probabilities under some certain choices of the claim amount distribution and the distribution of the inter-occurrence time of the claims.
Keywords: Integral equation, renewal process, integro-differential equation, ruin probability, negative risk sums., survival probability.
Mathematics Subject Classification: 62P05; 60K0.
Citation: Yinghui Dong, Guojing Wang. Ruin probability for renewal risk model with negative risk sums. Journal of Industrial & Management Optimization, 2006, 2 (2) : 229-236. doi: 10.3934/jimo.2006.2.229
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