Optimal Control of Diffusion Coefficients via Decoupling Fields | Zendy

Stefan Ankirchner | Zendy; Alexander Fromm | Zendy

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Optimal Control of Diffusion Coefficients via Decoupling Fields

Author(s) -

Stefan Ankirchner,

Alexander Fromm

Publication year - 2018

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/17m1152401

Subject(s) - mathematics , decoupling (probability) , stochastic differential equation , optimal control , maximum principle , stochastic control , pontryagin's minimum principle , diffusion , adjoint equation , mathematical analysis , control theory (sociology) , differential equation , control (management) , mathematical optimization , physics , computer science , control engineering , artificial intelligence , engineering , thermodynamics

We consider a diffusion control problem where the controller totally determines the stateu0027s diffusion coefficient but has no influence on the stateu0027s drift rate. By using the Pontryagin maximum principle we characterize an optimal control in terms of the adjoint forward-backward stochastic differential equation (FBSDE), turning out to be fully coupled. We use the method of decoupling fields for proving that the adjoint FBSDE possesses a solution.

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