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

作者：Tsai Cary Chi Liang^*; Lu Yi

来源：Scandinavian Actuarial Journal, 2010, (3): 200-220.

DOI：10.1080/03461230903112190

• Surplus process
• Diffusion process
• Ruin probability
• Maximal aggregate loss
• Compound geometric distribution
• Ordering
• Bound

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.

• 出版日期2010