BSDEs with singular terminal condition and control problems with constraints
Optimization and Control
2013-06-04 v2 Probability
Trading and Market Microstructure
Abstract
We provide a probabilistic solution of a not necessarily Markovian control problem with a state constraint by means of a Backward Stochastic Differential Equation (BSDE). The novelty of our solution approach is that the BSDE possesses a singular terminal condition. We prove that a solution of the BSDE exists, thus partly generalizing existence results obtained by Popier in [7] and [8]. We perform a verification and discuss special cases for which the control problem has explicit solutions.
Keywords
Cite
@article{arxiv.1305.6541,
title = {BSDEs with singular terminal condition and control problems with constraints},
author = {Stefan Ankirchner and Monique Jeanblanc and Thomas Kruse},
journal= {arXiv preprint arXiv:1305.6541},
year = {2013}
}