指数索赔情形下一类相依两险种风险模型的破产概率

考虑一类稀疏过程下索赔相依的两险种风险模型:U(t)=u+ct-∑i=1N2(t)X_i-∑i=1N2(t)Y_(i),其中{N_1(t),t≥0}、{N_2(t),t≥0}分别表示两个险种的索赔次数,它们按下述方式相关:N_1(t)N_(11)(t)+N_(12)(t),N_2(t)=N_(22)(t)+N'_(12)(t),{N'_(12)(t),t≥0}是{N_(12)(t),t≥0}的一个p-稀疏.考虑下列两种情形:(Ⅰ){N_(11)(t),t≥0}、{N_(12)(t),t≥0}、{N_(22)(t),t≥0}均为Poisson过程;(Ⅱ){N_(11)(t),t≥0}、{N_(22)(t),t≥0}为Poisson过程,{N_(12)(t),t≥0}为Erlang(2)过程.在上述两种情形下,当两险种的单次索赔额均服从指数分布时,通过建立并求解生存概率所满足的微分方程,给出其破产概率的表达式.

The Ruin Probability for a Class of Bivariate Risk Model with Correlated Aggregate Claims in the Case of Exponential Claims

The paper considers a class of bivariate risk model with correlated aggregate Wi(0 AT2(t)claims under sparse process as follows:U(t) = u+ct- sum from i=1 to (N_1(t))(1/n)X_i—sum from i=1 to(N_2(t))(1/n),Yi,where {Ni(t),t≥ 0}is the claim number processes for class i,i = 1,2.{N_1(t),t≥0},{N_2(t),t≥0} are correlated in the way that N_1(t) = N_(11)(t) + N_(12)(t),N_2(t) = N_(22)(t) + N′_(12)(t),where {N′_(12)(t),t ≥ 0} is a p— sparse process of {N_(12)(t),t ≥0}.We derive the exact expression of ruin probability when claims follow the exponential distributions in the following two cases:(I) {N_(11)(t),t≥0},{N_(12)(t),t ≥ 0},{N_(22)(t),t ≥ 0} are all Poisson processes;(II) {N_(11)(t),t ≥ 0}、{N_(22)(t),t ≥0} are both Poisson processes,and {N_(12)(t),t ≥ 0} is an Erlang(2) process.