本项目拟利用随机最大值原理和倒向随机微分方程理论深入研究(非马氏)随机参数保险模型下的若干随机优化问题。我们首先利用仿射扩散模型来刻画市场的风险价格过程，进而研究该市场模型下保险人的均值-方差再保险与投资问题；其次，我们将进一步研究时间不一致性偏好下保险人的最优决策问题并探讨均衡策略的唯一性；最后，我们将同时考虑保险人和再保险人的利益，在Stackelberg博弈(即，Leader-Follower博弈)框架下研究最优再保险与投资问题，其中再保险人是博弈的领导者，而保险人是追随者。Stackelberg博弈模型的引入可以完美刻画保险人和再保险人在保险市场中地位的不对称性。该项目的研究内容是金融保险和随机控制领域的最新课题，它不仅可以丰富倒向随机微分方程的相关结果，同时也将极大促进随机控制、数理金融与精算等其他理论的发展。

This project intends to study several stochastic optimization problems for (non-Markovian) insurance risk models with random parameters by using stochastic maximum principles and backward stochastic differential equations. We first characterize the market price of risk by an affine diffusion factor process and then study the mean-variance reinsurance and investment problem. Secondly, we further study a kind of time inconsistent optimal control problems for insurers and discuss the uniqueness of the equilibrium strategy. Finally, we study the optimal reinsurance and investment problem from the perspectives of both an insurer and a reinsurer in the framework of a Stackelberg game (i.e., a Leader-Follower game) and assume that the reinsurer and the insurer are the leader and the follower of the game, respectively. Stackelberg game is perfect for characterizing the unequal power of the two parties in the insurance market. All the problems considered in this project are new subjects in stochastic control, finance and insurance. The study of these problems not only enriches the contents of backward stochastic differential equations, but also promotes the development of other theories such as stochastic optimal control, mathematical finance and actuarial science.