BSDEs with singular terminal condition and control problems with constraints

2013/05/28 by Ankirchner, Stefan, Jeanblanc, Monique, Kruse, Thomas · 3 citations
#FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Trading and Market Microstructure (q-fin.TR)

paper · doi:10.48550/arxiv.1305.6541

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.

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