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arXiv · 2005.06789

On the Stochastic Control-Stopping Problem

Brahim Asri·Said Hamadène·Khalid Oufdil
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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.

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Brahim Asri, Said Hamadène, Khalid Oufdil. 2020-05-14. On the Stochastic Control-Stopping Problem. https://arxiv.org/abs/2005.06789

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