Finite-Dimensional Representations for Controlled Diffusions with Delay

Journal Article · Sun Feb 15 00:00:00 EST 2015 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-014-9256-2· OSTI ID:22470059

Federico, Salvatore ^[1]; Tankov, Peter ^[2]

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1. Università di Milano, Dipartimento di Economia, Management e Metodi Quantitativi (Italy)
2. Université Paris Diderot, Laboratoire de Probabilités et Modèles Aléatoires (France)

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.

• OSTI ID: 22470059
• Journal Information: Applied Mathematics and Optimization, Vol. 71, Issue 1; Other Information: Copyright (c) 2015 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICAL METHODS AND COMPUTING
APPROXIMATIONS
DIFFERENTIAL EQUATIONS
DIFFUSION
ERRORS
MARKOV PROCESS
MATHEMATICAL SOLUTIONS
OPTIMAL CONTROL