OPTIMAL STOCHASTIC CONTROL PROBLEM UNDER MODEL UNCERTAINTY WITH NONENTROPY PENALTY

Wahid Faidi (), Anis Matoussi and Mohamed Mnif ()
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Wahid Faidi: Laboratoire de Modélisation Mathématique et Numérique, dans les Sciences de l’Ingénieur, ENIT, University of Tunis El Manar, Tunisia
Anis Matoussi: Laboratoire Manceau de Mathématiques, Institut du Risque et de l’Assurance, Université du Maine, US
Mohamed Mnif: Laboratoire de Modélisation Mathématique et Numérique, dans les Sciences de l’Ingénieur, ENIT, University of Tunis El Manar, Tunisia

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 03, 1-41

Abstract: In this paper, a stochastic control problem under model uncertainty with general penalty term is studied. Two types of penalties are considered. The first one is of type f-divergence penalty treated in the general framework of a continuous filtration. The second one called consistent time penalty is studied in the context of a Brownian filtration. In the case of consistent time penalty, we characterize the value process of our stochastic control problem as the unique solution of a class of quadratic backward stochastic differential equation with unbounded terminal condition.

Keywords: Robust stochastic control; model uncertainty; Knightian uncertainty; backward stochastic differential equations; utility maximization (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024917500157

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