论文标题
在具有跳跃簇的部分可观察模型中通过BSDE的最佳再保险
Optimal reinsurance via BSDEs in a partially observable model with jump clusters
论文作者
论文摘要
当损失过程表现出跳跃聚类功能并且保险公司有限制有关损失过程的信息时，我们研究了最佳再保险问题。我们最大程度地提高了终端财富的预期指数效用，并表明存在最佳解决方案。通过利用Kushner-Stratonovich和Zakai方法，我们提供了管理（无限维）过滤器的动力学的方程式，并在BSDE方面表征了随机优化问题的解决方案，为此我们证明了解决方案的存在和独特性。在讨论了一般再保险保费的最佳策略之后，我们在某些相关情况下提供了更明确的结果。
We investigate the optimal reinsurance problem when the loss process exhibits jump clustering features and the insurance company has restricted information about the loss process. We maximize expected exponential utility of terminal wealth and show that an optimal solution exists. By exploiting both the Kushner-Stratonovich and Zakai approaches, we provide the equation governing the dynamics of the (infinite-dimensional) filter and characterize the solution of the stochastic optimization problem in terms of a BSDE, for which we prove existence and uniqueness of solution. After discussing the optimal strategy for a general reinsurance premium, we provide more explicit results in some relevant cases.
