On minimizing the ruin probability by investment and reinsurance
On minimizing the ruin probability by investment and reinsurance
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DOI：
10.1214/aoap/1031863173
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发表时间：
2002-08
影响因子：
1.8
通讯作者：
Hanspeter Schmidli
中科院分区：
文献类型：
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作者：
Hanspeter Schmidli
我们考虑一个经典的风险模型，并允许投资到一个风险资产模型作为布莱克-斯科尔斯模型以及（比例）再保险。通过Hamilton-Jacobi-Bellman方法，我们找到了最优策略的候选项，并开发了求解HJB方程的数值过程。为了证明HJB方程的任何递增解是有界的，并解决了优化问题，我们证明了一个验证定理。证明了HJB方程存在一个递增解。最后讨论了两个数值算例。
We consider a classical risk model and allow investment into a risky asset modelled as a Black-Scholes model as well as (proportional) reinsurance. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal strategy and develop a numerical procedure to solve the HJB equation. We prove a verification theorem in order to show that any increasing solution to the HJB equation is bounded and solves the optimisation problem. We prove that an increasing solution to the HJB equation exists. Finally two numerical examples are discussed.