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Malliavin calculus and optimal control of stochastic Volterra equations
University Med Khider, Algeria. (Stochastic analysis and stochastic processes)
University of Oslo, Norway.
2015 (English)In: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 167, no 3, p. 1070-1094Article in journal (Refereed) Published
Abstract [en]

Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore, classical methods, such as dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that using Malliavin calculus, it is possible to formulate modified functional types of maximum principle suitable for such systems. This principle also applies to situations where the controller has only partial information available to base her decisions upon. We present both a Mangasarian sufficient condition and a Pontryagin-type maximum principle of this type, and then, we use the results to study some specific examples. In particular, we solve an optimal portfolio problem in a financial market model with memory.

Place, publisher, year, edition, pages
Springer, 2015. Vol. 167, no 3, p. 1070-1094
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-82299DOI: 10.1007/s10957-015-0753-5OAI: oai:DiVA.org:lnu-82299DiVA, id: diva2:1307458
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-05-07Bibliographically approved

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Agram, Nacira

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