现代保险金融风险模型中drawdown约束下的随机最优决策与鲁棒控制

随着金融全球化进程的加快，以及某些突发性公共卫生事件的出现，保险金融市场面临的风险变得日益复杂和多样化。因此，如何对各类风险进行有效建模，以及如何采取合理手段达到既规避风险又兼顾收益的目的已经成为保险金融行业亟待解决的问题。Drawdown作为衡量资产低于其历史最大财富程度的参考值，是常用的风险度量指标。大幅度的drawdown不仅意味着巨大的财富损失，还可能引发长期的经济萧条。该项目致力于利用随机过程和随机控制论思想来探讨风险模型中带drawdown约束的随机最优决策以及参数不确定情形下的鲁棒控制问题。主要在以下三个方面有所创新：1. 最小化drawdown概率准则下的鲁棒优化控制；2. drawdown约束下，最大化期望收益的随机最优控制；3.不同目标准则下，多人随机微分博弈的鲁棒均衡策略。该项目的系列研究不仅可以促进相关理论的发展，还将为保险、金融行业在市场决策时提供有价值的参考。

With the acceleration of the financial globalization progress, and the emergence of some unexpected public health events, the risks in insurance and financial market become more and more complicated and diversity. Therefore, to construct reasonable models for all kinds of risks, and to find the valid methods and techniques to reduce the risks as well as to increase the profit have become the very important research topic. Drawdown, measuring the decline of the value of a portfolio from its historic high-water mark, is a frequently quoted risk metric to evaluate the performance of portfolio managers in the fund-management industry. A significant drawdown not only indicates large losses but may also trigger a long-term recession. In this project, based on the theories of stochastic processes and stochastic control and the related methodologies, we focus on discussing the stochastic optimal control problems for the risk models with drawdown constraints and the robust control for the model with uncertainty in the insurance and financial market. We have the innovation on the following three points: 1. Robust control with the criterion of minimizing the probability of drawdown; 2. Stochastic optimal control which maximizes the expected profit with drawdown constraint; 3. Robust equilibrium strategy for multi-decision-maker within the stochastic differential game framework and under some different criteria. This research not only improves the development of the related theories, but also becomes the valuable reference for the decision-makers of the insurance and financial industry.