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Optimal position targeting via decoupling fields

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.
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https://hal.archives-ouvertes.fr/hal-01500311
Contributor : Alexandre Popier Connect in order to contact the contributor
Submitted on : Monday, April 16, 2018 - 9:50:59 AM
Last modification on : Saturday, June 13, 2020 - 8:20:05 PM

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  • HAL Id : hal-01500311, version 2

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Stefan Ankirchner, Alexander Fromm, Thomas Kruse, Alexandre Popier. Optimal position targeting via decoupling fields. 2018. ⟨hal-01500311v2⟩

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