稀疏过程下一类相依两险种风险模型的破产概率

Ruin Probabilities for One Class of Bivariate Risk Model with Correlated Aggregate Claims under Sparse Processes

  • 摘要: 本文考虑一类索赔相依的两险种风险模型, 其中两个索赔到达计数过程通过一个Erlang(2)过程部分稀疏相关. 通过引入辅助模型, 得到破产概率所满足的积分方程, 并借助于更新方法讨论其渐进性, 最后在索赔额均服从指数分布时给出该模型及辅助模型的生存概率所满足的线性微分方程组及其解法.

     

    Abstract: The paper considers a risk model with two dependent classes of insurance business. In this model, the two claim number processes are partly sparsely correlated through an Erlang(2) process. By introducing an auxiliary model, we obtain the integral equations for ultimate ruin probabilities, and discuss the asymptotic property of ruin probabilities by renewal approach. We also get the linear differential equations of ruin probabilities of the model and the corresponding auxiliary model when claims follow the exponential distributions, and show how solves the linear differential equations by a specific example.

     

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