报告题目： Set Valued HJB Equations
报 告 人： 张建丰 教授
报告人所在单位： 南加州大学
报告日期： 2023-07-18
报告时间： 14：00-15：00
报告地点： 光华东主楼1801
报告摘要：
The set values have been introduced for many applications, such as time inconsistent stochastic optimization problems, multivariate dynamic risk measures, and nonzero sum games with multiple equilibria. Among others, one crucial property of the dynamic set value is the dynamic programming principle. In this talk we introduce a notion of set valued PDEs and show that the set value function of certain multidimensional control problem is the unique solution to the corresponding set valued HJB equation. A key tool is the set valued Ito formula, which together with the DPP induces the PDE. In the one dimensional case, the set valued PDE reduces back to the standard HJB equations. Our characterization of the set values is through their boundaries, which are manifolds. Thus our approach is intrinsically connected to the existing theory of moving manifolds, such as front propagation and mean curvature flows. Roughly speaking, those equations can be viewed as first order set valued ODEs, and we extend them to second order PDEs. Another difference is that, due to different applications, those equations are forward in time (with initial conditions), while we consider backward equations (with terminal conditions). The talk is based on a joint work with Melih Iseri.
学术报告海报.pdf
本年度学院报告总序号： 908
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