An effective method for constructing bounds for ruin probabilities for the surplus process perturbed by diffusion |
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Authors: | Cary Chi-Liang Tsai Yi Lu |
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Affiliation: | 1. Department of Statistics and Actuarial Science , Simon Fraser University , Burnaby, BC V5A 1S6, Canada cltsai@sfu.ca;3. Department of Statistics and Actuarial Science , Simon Fraser University , Burnaby, BC V5A 1S6, Canada |
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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. |
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Keywords: | Surplus process Diffusion process Ruin probability Maximal aggregate loss Compound geometric distribution Ordering Bound |
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