论文标题
使用一般内部信息的保险公司强大的最佳投资和风险控制
Robust optimal investment and risk control for an insurer with general insider information
论文作者
论文摘要
在本文中，我们研究拥有有关模型不确定性下的内部信息和保险市场的保险公司的强大最佳投资和风险控制问题。财务风险资产流程和保险风险过程都被认为是非常普遍的跳跃扩散过程。内部信息是最通用的形式，而不是初始扩大类型。我们使用前向积分理论来赋予强大的最佳策略的上半年表征，并将预期的随机差异游戏问题转变为非期望的随机差异游戏问题。然后，我们采用随机最大原理来获得鲁棒策略的总表征。当保险公司是“小”和Malliavin Colculus的“小”和“大”时，我们讨论了两种典型情况。对于“小型”保险公司，我们在连续情况下获得了封闭形式的解决方案，并在跳高的情况下获得了一半的封闭式解决方案。对于“大型”保险公司，我们将问题减少到二次向后随机微分方程（BSDE），并在连续情况下获得封闭形式的解决方案，而无需模型不确定性。我们讨论了模型不确定性，内部信息和“大型”保险公司对最佳策略的一些影响。
In this paper, we study the robust optimal investment and risk control problem for an insurer who owns the insider information about the financial market and the insurance market under model uncertainty. Both financial risky asset process and insurance risk process are assumed to be very general jump diffusion processes. The insider information is of the most general form rather than the initial enlargement type. We use the theory of forward integrals to give the first half characterization of the robust optimal strategy and transform the anticipating stochastic differential game problem into the nonanticipative stochastic differential game problem. Then we adopt the stochastic maximum principle to obtain the total characterization of the robust strategy. We discuss the two typical situations when the insurer is `small' and `large' by Malliavin calculus. For the `small' insurer, we obtain the closed-form solution in the continuous case and the half closed-form solution in the case with jumps. For the `large' insurer, we reduce the problem to the quadratic backward stochastic differential equation (BSDE) and obtain the closed-form solution in the continuous case without model uncertainty. We discuss some impacts of the model uncertainty, insider information and the `large' insurer on the optimal strategy.
