DYNAMIC PROGRAMMING PRINCIPLE AND ASSOCIATED HAMILTON-JACOBI-BELLMAN EQUATION FOR STOCHASTIC RECURSIVE CONTROL PROBLEM WITH NON-LIPSCHITZ AGGREGATOR

作者：Pu, Jiangyan; Zhang, Qi^*

来源：ESAIM: Control, Optimisation and Calculus of Variations , 2018, 24(1): 355-376.

DOI：10.1051/cocv/2017016

• Stochastic recursive control problem
• non-Lipschitz aggregator
• dynamic programming principle
• Hamilton-Jacobi-Bellman equation
• continuous-time Epstein Zin utility
• viscosity solution

In this work we study the stochastic recursive control problem, in which the aggregator (or generator) of the backward stochastic differential equation describing the running cost is continuous but not necessarily Lipschitz with respect to the first unknown variable and the control, and monotonic with respect to the first unknown variable. The dynamic programming principle and the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman equation are established in this setting by the generalized comparison theorem for backward stochastic differential equations and the stability of viscosity solutions. Finally we take the control problem of continuous time Epstein Zin utility with non-Lipschitz aggregator as an example to demonstrate the application of our study.

• 出版日期2018-1
• 单位复旦大学