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April 2020 Optimal position targeting via decoupling fields
Stefan Ankirchner, Alexander Fromm, Thomas Kruse, Alexandre Popier
Ann. Appl. Probab. 30(2): 644-672 (April 2020). DOI: 10.1214/19-AAP1511


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. We exploit a monotonicity property of the decoupling field for solving the original constrained problem and characterize its solution in terms of an FBSDE with a free backward part.


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Stefan Ankirchner. Alexander Fromm. Thomas Kruse. Alexandre Popier. "Optimal position targeting via decoupling fields." Ann. Appl. Probab. 30 (2) 644 - 672, April 2020.


Received: 1 April 2017; Revised: 1 January 2019; Published: April 2020
First available in Project Euclid: 8 June 2020

zbMATH: 07236130
MathSciNet: MR4108118
Digital Object Identifier: 10.1214/19-AAP1511

Primary: 49J05, 60H99
Secondary: 60G99, 93E20

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.30 • No. 2 • April 2020
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