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.
Representation of non-markovian optimal stopping problems by constrained BSDEs with a single jump / M. Fuhrman, H. Pham, F. Zeni. - In: ELECTRONIC COMMUNICATIONS IN PROBABILITY. - ISSN 1083-589X. - 21:0(2016).
|Titolo:||Representation of non-markovian optimal stopping problems by constrained BSDEs with a single jump|
FUHRMAN, MARCO ALESSANDRO (Primo)
|Parole Chiave:||Backward stochastic differential equations; Optimal stopping; Randomized stopping; Statistics and Probability;|
|Settore Scientifico Disciplinare:||Settore MAT/06 - Probabilita' e Statistica Matematica|
|Data di pubblicazione:||2016|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1214/16-ECP4123|
|Appare nelle tipologie:||01 - Articolo su periodico|