摘要
在轻尾假设下,对保险公司盈余离散模型的期望折现罚金函数进行了研究.通过构造指数鞅,定义了新的测度.利用测度变换公式,消去了折现,得到新的期望折现罚金函数,简化了表达式,并且得到了其满足的更新方程.通过新测度下的期望折现罚金函数,得到Lundberg不等式;并利用测度变换,使得新测度下破产的发生变得确定,更新方程将简化为一般更新方程;进而利用关键更新定理,得到了当初始资本趋于无穷大时,期望折现罚金函数的渐进性;最后对于个体索赔额服从指数分布的特殊情况,导出其破产概率公式的显示表达式.
Under light-tail assumption, the expected company surplus is studied. By constructing index discount penalty function of discrete model for insurance martingale, the new measurement is defined. By using measurement change, the discount is removed, new expected discount penalty function is obtained, the expression is simplified and the new satisfied renewing equation is obtained. Through expected discount penalty function under new measurement, Lundberg Inequality is received, by using measurement change, the incidence of bankruptcy becomes determined under new measurement, the renewing equation is simplified to a general renewal equation, furthermore, the key renewing theorem is used to obtain the asymptotic of expected discount penalty function when initial capital tends to infinity. Finally, as for the special situation that individual claim amount following exponential distribution, the explicit expression of its ruin probability formula is derived.
出处
《重庆工商大学学报（自然科学版）》
2013年第6期11-15,共5页
Journal of Chongqing Technology and Business University:Natural Science Edition
