由于现实中决策者的偏好是不断变化的，因此，采用固定的偏好来分析和解决金融和保险中的最优决策问题是不恰当的。当考虑时间不一致性偏好时，由于不满足经典的动态规划准则，这导致了所谓的时间不一致的最优控制问题。本项目将采用博弈论的方法来研究金融和保险中带有时间不一致性偏好的最优决策问题。研究内容包括：1.含有一般贴现函数的最优分红问题，考虑保险人的破产风险，在跳—扩散和lévy风险模型下得到相应的均衡HJB方程及验证定理，并在具体的贴现函数下得到最优策略的解析解或数值解；2. 在含有Regime-Switching的Merton模型下考虑最优投资问题，假设决策者的偏好依赖于当前环境变量的状态，得到均衡HJB方程（组）并讨论该方程（组）的解的存在唯一性和数值解；3. 采用多人微分博弈和鞅方法来解决幂效用和指数效用函数下的含有随机参数的最优消费—投资问题，该问题将归结为研究一类新的倒向随机积分方程。

Since the preference of a decision-maker is changing all the time in real world, it is unreasonable to analyze and resolve optimal decision-making problems in finance and insurance by fixing his/her preference. Once considering the time-inconsistent preference, the classical dynamic programing principle does not hold, which leads to the so-called time-inconsistent optimal control problem. The project investigates some decision-making problems with time-inconsistent preferences in finance and insurance by using the method of game theory. The main problems considered in the project include: 1. Optimal dividend problem with a general discount function. We will consider the ruin risk of the insurer, derive the equilibrium HJB equation and verification theorem in the jump-diffusion risk model and lévy risk model, and obtain the analytical solution or numerical solution of optimal strategies for some specific discount functions. 2. Optimal investment problem in Merton's model with regime-switching. Under the assumption that the decision-maker's preference depends on the state of the environment variable, we obtain the system of equilibrium HJB equations and discuss the existence and uniqueness of the solution and the numerical solution of the system. 3.Using the multi-person differential game and martingale method to resolve the optimal consumption-investment problem with stochastic parameters. This problem boils down to studying a new type of backward stochastic integral equation.