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Optimal position targeting via decoupling fields

Alexander Fromm
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Thomas Kruse
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Alexandre Popier


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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Dates and versions

hal-01500311 , version 1 (03-04-2017)
hal-01500311 , version 2 (16-04-2018)


  • HAL Id : hal-01500311 , version 2


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