基于跳扩散过程的Omega模型

文章通过在Omega模型中加入布朗运动扰动项,提出了一种跳扩散Omega破产模型.在索赔额为指数分布的情形下,给出了破产率函数是常数时的破产概率函数表达式.文章进一步研究了破产概率和盈余过程的“负占有时”之间的关系,并给出了破产概率函数的第二种推导过程.最后通过两个数值试验,将我们的模型与Albreeher和Lautscham (2013)的Omega模型的破产概率进行了比较分析.

Omega Model for a Jump-Diffusion Process

A jump-diffusion Omega model is studied in this paper. In thismodel, the surplus process is a perturbation of a compound Poisson process by a Brownmotion. For exponential claim size and constant bankruptcy rate function, severalexplicit formulae on bankruptcy probability for the model are derived. The relationshipbetween bankruptcy probability and occupation time in the red is also discussed. Thennumerical examples are given to show some comparisons for the model with the Omega modelof Albrecher and Lautscham (2013).