Interest-Bearing Surlus Model with Liquid Reserves

Kristina P. Sendova and Yanyan Zheng

Journal of Insurance Issues, 2010, vol. 33, issue 2, 178-196

Abstract: We consider a ruin model where the surplus process of an insurance company is constructed so that part of the current surplus is kept available at all times and the remaining part is invested. The former portion of the capital is called “liquid reserves.” In this paper, we study the expected discounted penalty function at ruin. First, we derive an integro-differential equation satisfied by the Gerber-Shiu function. Second, we apply Laplace transforms to the equation and reduce it to a first order linear differential equation for the function in question. Finally, we find an explicit form of the Gerber-Shiu function by considering exponential claims.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:wri:journl:v:33:y:2010:i:2:p:178-196

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