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- Title
Malliavin Calculus and Optimal Control of Stochastic Volterra Equations.
- Authors
Agram, Nacira; Øksendal, Bernt
- 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.
- Subjects
NUMERICAL solutions to Voterra equations; OPTIMAL control theory; MALLIAVIN calculus; MAXIMUM principles (Mathematics); PONTRYAGIN'S minimum principle; FINANCIAL markets; MATHEMATICAL models
- Publication
Journal of Optimization Theory & Applications, 2015, Vol 167, Issue 3, p1070
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-015-0753-5