三类索赔额分布下的破产概率的模拟值及其R实现

破产概率的计算是精算破产理论的经典问题,对当前保险经营风险的度量有重要的理论意义和参考价值。在以往对破产概率的研究中,出于理论分析的方便,往往假设索赔额分布具有特殊的形式,而对更复杂的索赔额分布,求出理论上的解析解往往是不可行的,为此需要求解数值解。随机模拟是很重要的一种求数值解的方法。本文考虑三类索赔额分布:伽玛分布、对数正态分布、逆高斯分布,对每类分布,通过模拟不同参数下的索赔额,得到破产频数、首次破产对应的索赔次数的期望及标准差,并运用R软件对不同索赔额分布下的模拟结果进行比较分析。

The calculation of ruin probability is the classical problem in actuarial ruin theory. As one of the important indices to measure current insurance operational risk, to quantify the ruin probability has important theoretical significance and reference value. In the past study on ruin probability, for the sake of convenience as to theoretical analysis, it is often assumed that the claim amount has a special distribution form. But with more complex claim amount distribution, one needs to obtain the numerical solution since the theoretical analytic solutions are often infeasible. Stochastic simulation is a very important method to numerical solution. In this paper, we consider three claim amount distributions： gamma distribution, lognormal distribution, and inverse Gaussian distribution. For each distribution, by simulating the claim amount with different parameters, we obtain the ruin frequency, the mean and standard deviation of the claim number corresponding to the first ruin. We conclude the paper by comparing with the simulation results under different claim amount distributions.