Malliavin Calculus and Optimal Control of Stochastic Volterra Equations

Nacira Agram () and Bernt Øksendal ()
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Nacira Agram: University Med Khider
Bernt Øksendal: University of Oslo

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 3, No 18, 1070-1094

Abstract: Abstract 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.

Keywords: Stochastic Volterra equations; Partial information; Malliavin calculus; Maximum principle; Primary 60H07; 60H20; 93E20 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-015-0753-5

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