摘要
研究了更新风险模型中的渐近破产概率,其中允许保险公司将其资产按常数比例投资于满足几何布朗运动的股票市场,其余部分投资于非负利率的债券市场.对此模型假定索赔额满足正则分布且两两拟渐近独立,根据伊藤公式,给出保险公司资产的表达式,并最后给出了有限时间和无限时间的破产概率.当更新过程的特殊情况即复合泊松过程且索赔额独立同分布时,得出最终破产概率简洁的渐近表达式,与文献[Gaier J,Grandits P.Ruin probabilities and investment underinterest force in the presence of regularly varying tails.Scand Actuarial J,2004(4):256-278]中得到结果一样,并给出了模拟的结果.
The asymptotic behavior of ruin probabilities was investigated in a renewal risk model, in which the insurance company is allowed to invest a constant fraction of its wealth in a stock market which is described by a geometric Brownian motion and the remaining wealth in a bond with nonnegative interest force. For this model, in the presence of pairwise quasi-asymptotic independent and regularly-varying- tailed claims, the expression of the wealth process was derived by ho formula, and then the finite-time and ultimate ruin probabilities were obtained. Specially, in the compound Poisson model with independent and identically distributed claims, explicit asymptotic expression ~or the ultimate ruin probability was given, which is just the same as Ref. [-Gaier J, Grandits P. Ruin probabilities and investment under interest force in the presence of regularly varying tails. Scand Actuarial J, 2004（4） ： 256- 278]. Finally, some numerical results were given.
基金
国家自然科学基金(10801124
11171321)
中央高校基本科研业务费专项基金资助
关键词
破产概率
两两拟渐近独立
利息力
正则变换
几何布朗运动
ruin probabilities
pairwise quasi-asymptotic independence
interest force
regular variation
geometric Brownian motion
