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具有两类索赔干扰风险模型的Gerber-Shiu函数
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Abstract:
考虑一个受布朗运动扰动的两类索赔风险模型，两个索赔过程分别是独立的泊松过程和广义Erlang(2)过程。以Gerber-Shiu函数为研究对象，首先得到了由索赔导致破产和扰动导致破产的两种情况下惩罚函数满足的积分–微分方程及拉普拉斯变换的表达式。当两类的索赔额均呈指数分布时，给出了一个具体的数值例子。
Consider a two-class claim risk model perturbed by Brownian motion, where the two claim processes are independent Poisson process and generalized Erlang(2) process respectively. Taking the Gerber-Shiu function as the research object, the integral-differential equations and the Laplace transform expressions satisfied by the penalty functions in the cases of ruin caused by claims and perturbation are obtained first. When the claim amounts of both classes follow an exponential distribution, a specific numerical example is given.
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