本项目拟利用随机过程、随机分析与随机控制理论深入研究马尔科夫体制转换与传染金融保险模型下的定价与随机控制问题 。我们首先通过等价鞅无套利定价理论、动态规划原理、随机极大值原理研究传染金融保险模型下的债券期权等衍生品定价问题与以期望效应最大化及均值方差为目标的随机最优控制问题。其次，我们将进一步研究受通货膨胀与随机利率影响的马尔科夫体制转换与传染金融保险市场模型中的金融衍生品定价与以期望效应最大化为目标的随机最优控制问题。再者，我们将利用随机控制与倒向随机微分方程相关理论推出马尔科夫体制转换与传染模型平均场随机控制问题的随机极大值原理，并将该模型下多个参与者的博弈问题应用到金融保险领域中的系统性风险研究。最后，我们将利用非线性期望与随机微分博弈相关理论解决马尔科夫体制转换与传染模型下的鲁棒随机最优控制问题。本项目的研究将促进随机最优控制、数理金融与精算等其他交叉领域理论的发展。

This project intends to study the pricing and stochastic control problems of Markov regime-switching and contagion finance and insurance model by using the theories of stochastic processes, stochastic analysis, and stochastic control. We first study the problems of bonds options pricing and stochastic optimal control with the objective function of maximization expectation and mean variance under the contagion finance and insurance model through the equivalence martingale arbitrage pricing theory, the dynamic programming principle and the stochastic maximum principle. Secondly, we further study the derivatives pricing problems and expected utility maximizing stochastic control problems in the Markov regime-switching and contagion finance and insurance model, which is affected by inflation and stochastic interest rate. Furthermore, we will use the theory of stochastic control and backward stochastic differential equations to deduce the stochastic maximum principle for mean field stochastic control problem under the Markov regime-switching and contagion model. We also apply the game problem of multiple participants in the above model to study the systematic risk in the fields of finance and insurance. Finally, we will use the nonlinear expectation and stochastic differential game theory to solve the problem of robust stochastic optimal control under Markov regime-switching and contagion model. The research of this project will promote the development of other theories such as stochastic optimal control, mathematical finance and actuarial.