English

On the Stochastic Control-Stopping Problem

Optimization and Control 2020-05-15 v1 Probability

Abstract

We study the stochastic control-stopping problem when the data are of polynomial growth. The approach is based on backward stochastic dierential equations (BSDEs for short). The problem turns into the study of a specic reected BSDE with a stochastic Lipschitz coecient for which we show existence and uniqueness of the solution. We then establish its relationship with the value function of the control-stopping problem. The optimal strategy is exhibited. Finally in the Markovian framework we prove that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation.

Keywords

Cite

@article{arxiv.2005.06789,
  title  = {On the Stochastic Control-Stopping Problem},
  author = {Brahim Asri and Said Hamadène and Khalid Oufdil},
  journal= {arXiv preprint arXiv:2005.06789},
  year   = {2020}
}
R2 v1 2026-06-23T15:32:20.503Z