周期注资的Lévy风险模型

Lévy Risk Model with Capital Injections and Periodic Observation

本文用Lévy过程为保险公司的盈余水平建模.假设保险公司在固定的时间对盈余水平进行观测,并在每次观测后做出决策.如果观察到的盈余水平小于给定的临界水平,且非负时,不足的部分将被一次性注入,使得盈余水平恢复到临界水平.如果观察到的盈余水平为负,就立即宣布破产.我们利用傅里叶余弦级数展开方法,提出了计算破产前有限时间期望折现注资总成本和有限时间期望折现罚函数的数值方法.通过误差分析和数值实例,证明了该方法的准确性和有效性,并研究了各个参数对结果的影响.

In this paper,the Lévy process is used to model the surplus level of an insurance company.It is assumed that the insurance company observes the surplus level at a fixed time and makes a decision after each observation.If the observed surplus level is less than a given critical level and is non-negative,the shortfall is injected once to bring the surplus level back to the critical level.If the observed surplus level is negative,ruin is declared immediately.Using the Fourier cosine series expansion method,we propose some numerical methods for computing the finite-time expected total discounted cost of capital injections before ruin and the finite-time expected discounted penalty function.The accuracy and efficiency of the method are demonstrated through error analysis and numerical examples,and the effect of each parameter on the results is studied.