Abstract:In this paper, we study the stochastic recursive optimal control problem under non-Lipschitz settings. More precisely, we suppose that the generator of G-BSDE describing the running cost is uniformly continuous and monotonic with respect to the first unknown variable. Using the comparison theorem for G-BSDE and the stability of viscosity solutions, we establish the dynamic programming principle and the connection between the value function and the viscosity solution of the associated Hamilton-Jacobi-Bellman equation. We provide an example of continuous time Epstein-Zin utility to demonstrate the application of our study.
From: Qiangjun Tang [view email]
[v1]
Mon, 25 Aug 2025 07:19:39 UTC (36 KB)
[v2]
Wed, 3 Dec 2025 06:41:09 UTC (36 KB)
[v3]
Fri, 10 Apr 2026 01:29:37 UTC (1 KB) (withdrawn)
[v4]
Mon, 13 Apr 2026 01:32:25 UTC (1 KB) (withdrawn)
[v5]
Sat, 15 Aug 2026 00:54:12 UTC (30 KB)
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