2022/05/06 by Jiaqiang Wen, Zhenhua Wu, Wen, Jiaqiang +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #60H10 #90C39 #93E20 #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2205.03052
openalex publication_date 2022/05/06 · openalex created_date 2022/05/11 · openalex updated_date 2026/07/28
In this paper, we study the delayed stochastic recursive optimal control problem with a non-Lipschitz generator, in which both the dynamics of the control system and the recursive cost functional depend on the past path segment of the state process in a general form. First, the dynamic programming principle for this control problem is obtained. Then, by the generalized comparison theorem of backward stochastic differential equations and the stability of viscosity solutions, we establish the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Finally, an application to the consumption-investment problem under the delayed continuous-time Epstein-Zin utility with a non-Lipschitz generator is presented.