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2016 Representation of non-Markovian optimal stopping problems by constrained BSDEs with a single jump
Marco Fuhrman, Huyên Pham, Federica Zeni
Electron. Commun. Probab. 21(none): 1-7 (2016). DOI: 10.1214/16-ECP4123

Abstract

We consider a non-Markovian optimal stopping problem on finite horizon. We prove that the value process can be represented by means of a backward stochastic differential equation (BSDE), defined on an enlarged probability space, containing a stochastic integral having a one-jump point process as integrator and an (unknown) process with a sign constraint as integrand. This provides an alternative representation with respect to the classical one given by a reflected BSDE. The connection between the two BSDEs is also clarified. Finally, we prove that the value of the optimal stopping problem is the same as the value of an auxiliary optimization problem where the intensity of the point process is controlled.

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Marco Fuhrman. Huyên Pham. Federica Zeni. "Representation of non-Markovian optimal stopping problems by constrained BSDEs with a single jump." Electron. Commun. Probab. 21 1 - 7, 2016. https://doi.org/10.1214/16-ECP4123

Information

Received: 18 February 2015; Accepted: 7 January 2016; Published: 2016
First available in Project Euclid: 3 February 2016

zbMATH: 1338.60118
MathSciNet: MR3485372
Digital Object Identifier: 10.1214/16-ECP4123

Subjects:
Primary: 60G40, 60H10

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