基于鲁棒优化的时间不一致性偏好下最优投资-再保险策略研究

The optimal investment and reinsurance problem is one of the core problems of modern risk theory. The evolution of the financial markets all over the world continues to accelerate, so that the feature of model parameter become uncertain and the strategy of the static optimization become lagging. It poses substantial challenges for the existing risk management theories and methods of the optimal investment and reinsurance problem. The project is designed for new ideas and methods to the model uncertainty of the risk model by using robust optimization, then seek new investment-reinsurance strategies under optimization criteria with time inconsistency. Considering the new situation of the insurance industry development, we study some risk models with following features: the decision-maker gives consideration to both the insurer and the reinsurer, the insurance company invests in an international economy and there is jump risk in the financial markets models. Because of the model uncertainty and the time inconsistency of the optimal objective, we solve the optimal strategies by combining the equilibrium idea in game theory with the robust optimization. Finally, in order to understand the robustness and the good properties, we will compare the equilibrium strategies we achieved with the existing strategies by numerical analysis method and empirical approach. This study combines well with the stochastic differential games theory and the robust optimization theory, build a research system of the dynamic optimization with the time inconsistency, and will contribute to providing a firm theoretical basis and operational guidance for investment and reinsurance decisions in China's insurance.

最优投资及再保险问题是现代风险理论的核心内容之一。由金融市场的快速演变等特征所导致的模型参数不确定性以及静态优化策略的时滞性，使传统的投资-再保险风险管理研究面临极大挑战。基于此，本项目致力于构建能够应对模型不确定性的风险模型的鲁棒优化框架，并寻找时间不一致性优化准则下的投资-再保险策略。我们结合当前保险业发展的新态势，研究具有如下特点的风险管理模型：兼顾保险公司和再保险公司双方收益、保险公司进行海外投资及风险资产带跳跃风险。为实现时间不一致性优化目标，并消除模型不确定性对策略选取的影响，采取将均衡博弈与鲁棒优化相结合的方式求解最优策略。最后，通过数值分析结合实证研究的方式，将现有风险模型的最优策略与所求均衡策略进行比较分析，验证其稳健性和优越性。本研究将随机微分博弈理论与鲁棒优化理论有机结合，形成针对时间不一致性优化目标的研究体系，并为我国保险业的投资、再保险决策提供理论依据及业务指导。

最优投资及再保险问题是现代风险理论的核心内容之一。本项目致力于构建能够应对模型不确定性的风险模型的鲁棒优化框架，把“相对熵”惩罚的鲁棒控制思想与随机控制理论结合起来，主要围绕“均值-方差准则”和“终端时刻财富期望效用最大化”这两个优化目标开展研究。在不同的金融保险模型中，利用动态规划、正倒向随机微分方程、鞅方法、博弈方法等现代随机控制理论的技术手段，研究了一些时间不一致问题的均衡最优投资再保险策略，也研究了一些时间一致性问题的稳健最优投资再保险策略及保险风险理论的相关问题。丰富了风险管理和精算理论，有利于我国保险业的投资、再保险决策部门寻找理论依据。