Optimal reinsurance via BSDEs in a partially observable model with jump clusters
研究了保险公司在损失过程具有跳跃聚类特征且信息受限时的最优再保险问题，通过BSDE刻画最优策略并证明存在唯一解。
Abstract We investigate an optimal reinsurance problem when the loss process exhibits jump clustering features and the insurance company has restricted information about the loss process. We maximise expected exponential utility of terminal wealth and show that an optimal strategy exists. By exploiting both the Kushner–Stratonovich and Zakai approaches, we provide the equation governing the dynamics of the (infinite-dimensional) filter and characterise the solution of the stochastic optimisation problem in terms of a BSDE, for which we prove existence and uniqueness of a solution. After discussing the optimal strategy for a general reinsurance premium, we provide more explicit results in some relevant cases.