论文标题
最大程度地降低Sparre Andersen模型下的废墟概率
Minimizing the Ruin Probability under the Sparre Andersen Model
论文作者
论文摘要
在本文中，我们考虑了将剩余过程遵循Sparre Andersen模型的保险公司的破坏可能性最小化的问题。类似于Bai等。 \ cite {bai2017optimal}，我们通过添加另一个维度来代表自上次索赔以来经过的时间来重新解决这个问题。 Markovization后，我们研究了值函数的规律性属性，并陈述了动态编程原理。此外，我们表明该值函数是相关的汉密尔顿 - 雅各比 - 贝尔曼方程的独特约束粘度解决方案。应该注意的是，我们的论文中没有折扣因素，这使证明独特性很难。为了克服这一困难，我们构建了严格的粘度超溶液。然后，我们比较了超级粘度的效率和订阅，而是比较了超级分析和严格的订阅。最终，我们表明所有粘度订阅均小于超级分解。
In this paper, we consider the problem of minimizing the ruin probability of an insurance company in which the surplus process follows the Sparre Andersen model. Similar to Bai et al. \cite{bai2017optimal}, we recast this problem in a Markovian framework by adding another dimension representing the time elapsed since the last claim. After Markovization, We investigate the regularity properties of the value function and state the dynamic programming principle. Furthermore, we show that the value function is the unique constrained viscosity solution to the associated Hamilton-Jacobi-Bellman equation. It should be noted that there is no discount factor in our paper, which makes it tricky to prove the uniqueness. To overcome this difficulty, we construct the strict viscosity supersolution. Then instead of comparing the usual viscosity supersolution and subsolution, we compare the supersolution and the strict subsolution. Eventually we show that all viscosity subsolution is less than the supersolution.
