具有线性红利界限的破产理论

The Ruin Theory in the Presence of a Linear Dividend Barrier

本文讨论了存存线性红利界限的带随机干扰的经典风险模型,给出了破产概率的一个上界,并证明了生存概率及红利付款的期望现值分别满足一个积分-微分方程。最后给出了索赔额服从指数分布时生存概率及红利付款的期望现值的确切表达式。

This paper discusses the classical risk model perturbed by diffusion in the presence of a linear dividend barrier. An upper bound of ruin probability is given. Furthermore, we show that the survival probability and the expectation of the discounted dividend payments fulfill integro-differential equations, respectively. Finally, the explicit formulae for them are derived when the claim size is exponentially distributed.