An effective method for constructing bounds for ruin probabilities for the surplus process perturbed by diffusion

Cary Tsai and Yi Lu

Scandinavian Actuarial Journal, 2010, vol. 2010, issue 3, 200-220

Abstract: In this paper, we first study orders, valid up to a certain positive initial surplus, between a pair of ruin probabilities resulting from two individual claim size random variables for corresponding continuous time surplus processes perturbed by diffusion. The results are then applied to obtain a smooth upper (lower) bound for the underlying ruin probability; the upper (lower) bound is constructed from exponentially distributed claims, provided that the mean residual lifetime function of the underlying random variable is non-decreasing (non-increasing). Finally, numerical examples are given to illustrate the constructed upper bounds for ruin probabilities with comparisons to some existing ones.

Date: 2010
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DOI: 10.1080/03461230903112190

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