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A Hida-Malliavin white noise calculus approach to optimal control
University of Oslo, Norway;University of Biskra, Algeria. (Stochastic analysis and stochastic processes)
University of Oslo, Norway.
2018 (English)In: Infinite Dimensional Analysis Quantum Probability and Related Topics, ISSN 0219-0257, Vol. 21, no 3, article id 1850014Article in journal (Refereed) Published
Abstract [en]

The classical maximum principle for optimal stochastic control states that if a control û is optimal, then the corresponding Hamiltonian has a maximum at u = û. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently, it was discovered by Shige Peng (still assuming no jumps) that one could also allow the diffusion coefficient to depend on the control, provided that the corresponding adjoint backward stochastic differential equation (BSDE) for the first-order derivative was extended to include an extra BSDE for the second-order derivatives. In this paper, we present an alternative approach based on Hida-Malliavin calculus and white noise theory. This enables us to handle the general case with jumps, allowing both the diffusion coefficient and the jump coefficient to depend on the control, and we do not need the extra BSDE with second-order derivatives. The result is illustrated by an example of a constrained linear-quadratic optimal control.

Place, publisher, year, edition, pages
World Scientific, 2018. Vol. 21, no 3, article id 1850014
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-82296DOI: 10.1142/S0219025718500145OAI: oai:DiVA.org:lnu-82296DiVA, id: diva2:1307455
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-05-06Bibliographically approved

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  • nn-NB
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  • Other locale
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  • text
  • asciidoc
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