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Malliavin Calculus and Optimal Control of Stochastic Volterra Equations

Agram, Nacira ; Øksendal, Bernt

Journal of optimization theory and applications, 2015-12, Vol.167 (3), p.1070-1094 [Periódico revisado por pares]

New York: Springer US

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Título:
Malliavin Calculus and Optimal Control of Stochastic Volterra Equations
Autor: Agram, Nacira ; Øksendal, Bernt
Assuntos: Applications of Mathematics ; Calculus ; Calculus of Variations and Optimal Control; Optimization ; Dynamic programming ; Dynamical systems ; Engineering ; Integral equations ; Matematik ; Mathematical analysis ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Maximum principle ; Operations Research/Decision Theory ; Optimal control ; Optimization ; Stochastic models ; Stochasticity ; Studies ; Theory of Computation
É parte de: Journal of optimization theory and applications, 2015-12, Vol.167 (3), p.1070-1094
Notas: ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
Descrição: 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.
Editor: New York: Springer US
Idioma: Inglês;Norueguês

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Malliavin Calculus and Optimal Control of Stochastic Volterra Equations

Agram, Nacira ; Øksendal, Bernt

New York: Springer US

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