Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 21 (2016), paper no. 3, 7 pp.
Representation of non-Markovian optimal stopping problems by constrained BSDEs with a single jump
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.
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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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