论文标题
投资损害概率：平滑度，IDE和ODE，渐近行为
Ruin probabilities with investments: smoothness, IDE and ODE, asymptotic behavior
论文作者
论文摘要
当一家拥有两个业务分支机构（人寿保险和非生活保险）的保险公司将其储备投资于风险的资产时，该研究涉及废墟问题，并通过几何布朗尼动议给出的价格动态。我们证明了废墟概率的平稳性是初始资本的函数，并为其获得了从经典意义上理解的全差异方程。对于指数分布的跳跃，我们表明生存概率是第四阶的普通微分方程的解决方案。对后者的渐近分析得出的结论是，毁灭概率衰减降至零，其方式与已经研究的模型案例相同。
The study deals with the ruin problem when an insurance company having two business branches, life insurance and non-life insurance, invests its reserve into a risky asset with the price dynamics given by a geometric Brownian motion. We prove a result on smoothness of the ruin probability as a function of the initial capital and obtain for it an integro-differential equation understood in the classical sense. For the case of exponentially distributed jumps we show that the survival probability is a solution of an ordinary differential equation of the 4th order. Asymptotic analysis of the latter leads to the conclusion that the ruin probability decays to zero in the same way as in the already studied cases of models with one-side jumps.
