Optimal position targeting via decoupling fields

Stefan Ankirchner, Alexander Fromm (), Thomas Kruse () and Alexandre Popier ()
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Stefan Ankirchner: Institut für Mathematik - Friedrich-Schiller-Universität = Friedrich Schiller University Jena [Jena, Germany]
Alexander Fromm: Institut für Mathematik - Friedrich-Schiller-Universität = Friedrich Schiller University Jena [Jena, Germany]
Thomas Kruse: Universität Duisburg-Essen = University of Duisburg-Essen [Essen]
Alexandre Popier: LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université

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Abstract: We consider a variant of the basic problem of the calculus of variations, where the Lagrangian is convex and subject to randomness adapted to a Brownian filtration. We solve the problem by reducing it, via a limiting argument, to an unconstrained control problem that consists in finding an absolutely continuous process minimizing the expected sum of the Lagrangian and the deviation of the terminal state from a given target position. Using the Pontryagin maximum principle we characterize a solution of the unconstrained control problem in terms of a fully coupled forward-backward stochastic differential equation (FBSDE). We use the method of decoupling fields for proving that the FBSDE has a unique solution.

Keywords: Optimal stochastic control; calculus of variations; forward backward stochastic differential equation; decoupling field (search for similar items in EconPapers)
Date: 2018-04-16
Note: View the original document on HAL open archive server: https://hal.science/hal-01500311v2
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