时 间：2026年04月24 日（周五）14：30 - 15：30
地 点：普陀校区理科大楼A1514室
报告人：王奕可 重庆工商大学讲师
主持人：危佳钦 华东师范大学教授
摘 要：
We focus on a class of time-inconsistent stochastic control problems, where the objective function includes the mean and several higher-order central moments of the terminal value of state. To tackle the time-inconsistency, we seek both the closed-loop and the open-loop Nash equilibrium controls as time-consistent solutions. We establish a partial differential equation (PDE) system for deriving a closed-loop Nash equilibrium control, which does not include the equilibrium value function. In deriving an open-loop Nash equilibrium control, we make some moment estimates in addition to the standard perturbation argument for developing a maximum principle. Then, the problem is reduced to solving a flow of forward-backward stochastic differential equations. In particular, we investigate linear controlled dynamics and some objective functions affine in the mean. In many cases, the closed-loop and the open-loop Nash equilibrium controls are identical, which are independent of the state value, the random path, and the preference on the odd-order central moments. By sending the highest order of central moments to infinity, we obtain the time-consistent solutions to some control problems whose objective functions include some penalty functions for deviation. In addition, we explore many solvable instances including a mean-variance-excess kurtosis portfolio selection problem. Interestingly, we find that the mean-variance equilibrium strategy is an open-loop Nash equilibrium control for our general higher-order moment problem if and only if a homogeneity condition holds. In the case with random parameters, we show that the solution to the mean-variance-skewness problem is given by a quadratic BSDE.
报告人简介：
王奕可，现供职于重庆工商大学金融学院。2013~2022年在中央财经大学精算科学系先后取得本科、博士学位，同期取得中国准精算师资格。研究方向包含随机控制、保险精算、金融数学等。主持国家自然科学基金青年项目1项，主要研究成果发表在SIAM J. Control Optim.、Math. Oper. Res.、Finance Stoch.等名国际重要学术期刊上。王奕可，现供职于重庆工商大学金融学院。2013~2022年在中央财经大学精算科学系先后取得本科、博士学位，同期取得中国准精算师资格。研究方向包含随机控制、保险精算、金融数学等。主持国家自然科学基金青年项目1项，主要研究成果发表在SIAM J. Control Optim.、Math. Oper. Res.、Finance Stoch.等名国际重要学术期刊上。