A probabilistic max-plus numerical method for solving stochastic control problems

Marianne Akian 1, 2 Eric Fodjo 1, 2
1 TROPICAL - TROPICAL
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We consider fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite set-valued (or switching) control and possibly a continuum-valued control. We construct a lower complexity probabilistic numerical algorithm by combining the idempotent expansion properties obtained by McEneaney, Kaise and Han (2011) for solving such problems with a numerical probabilistic method such as the one proposed by Fahim, Touzi and Warin (2011) for solving some fully nonlinear parabolic partial differential equations. Numerical tests on a small example of pricing and hedging an option are presented.
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Conference papers
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https://hal.inria.fr/hal-01425344
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Submitted on : Tuesday, January 3, 2017 - 3:16:55 PM
Last modification on : Wednesday, March 27, 2019 - 4:08:32 PM

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  • HAL Id : hal-01425344, version 1
  • ARXIV : 1605.02816

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Marianne Akian, Eric Fodjo. A probabilistic max-plus numerical method for solving stochastic control problems. 55th Conference on Decision and Control (CDC 2016), Dec 2016, Las Vegas, United States. 〈hal-01425344〉

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