Electronic Communications in Probability

Representation of non-Markovian optimal stopping problems by constrained BSDEs with a single jump

Marco Fuhrman, Huyên Pham, and Federica Zeni

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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.

Article information

Electron. Commun. Probab., Volume 21 (2016), paper no. 3, 7 pp.

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

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Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60H10: Stochastic ordinary differential equations [See also 34F05]

optimal stopping backward stochastic differential equations randomized stopping

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Fuhrman, Marco; Pham, Huyên; Zeni, Federica. Representation of non-Markovian optimal stopping problems by constrained BSDEs with a single jump. Electron. Commun. Probab. 21 (2016), paper no. 3, 7 pp. doi:10.1214/16-ECP4123. https://projecteuclid.org/euclid.ecp/1454514623

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