论文标题
最大程度地减少通过再保险的指数巴黎废墟的折现概率
Minimizing the Discounted Probability of Exponential Parisian Ruin via Reinsurance
论文作者
论文摘要
我们研究了最大程度地减少指数级巴黎废墟的折现概率的问题，即保险公司的盈余表现出低于零以上的偏差的折扣概率。保险人通过根据均值变化的溢价原则来控制其盈余，如Liang，Liang和Young（2019）。我们考虑了经典的风险模型，并应用随机Perron的方法，如Bayraktar和Sirbu（2012,2013,2014）所介绍的那样，表明指数级的巴黎毁灭的最低折扣可能性是其Hamilton-Jacobi-Bellman方程与$ \ pm pm \ pm \ fly fly \ flouse $ \ flience $ \ ferty $ \ infty $ \ flouse $ \ flouse的独特粘度解决方案。证明比较原则的主要困难是由于哈密顿人的不连续性引起的。
We study the problem of minimizing the discounted probability of exponential Parisian ruin, that is, the discounted probability that an insurer's surplus exhibits an excursion below zero in excess of an exponentially distributed clock. The insurer controls its surplus via reinsurance priced according to the mean-variance premium principle, as in Liang, Liang, and Young (2019). We consider the classical risk model and apply stochastic Perron's method, as introduced by Bayraktar and Sirbu (2012,2013,2014), to show that the minimum discounted probability of exponential Parisian ruin is the unique viscosity solution of its Hamilton-Jacobi-Bellman equation with boundary conditions at $\pm \infty$. A major difficulty in proving the comparison principle arises from the discontinuity of the Hamiltonian.
