Stochastic Impulse Control of Non-Markovian Processes

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-009-9070-4· OSTI ID:21480279

Djehiche, Boualem ^[1]; Hamadene, Said; Hdhiri, Ibtissam ^[2]

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1. Royal Institute of Technology, Department of Mathematics (Sweden)
2. Universite du Maine, Departement de Mathematiques, Equipe Statistique et Processus (France)

We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of combined optimal stochastic and impulse control of a fairly general class of diffusions with random coefficients. Unlike, in the Markovian framework, we cannot apply quasi-variational inequalities techniques. We rather derive the main results using techniques involving reflected BSDEs and the Snell envelope.

• OSTI ID: 21480279
• Journal Information: Applied Mathematics and Optimization, Vol. 61, Issue 1; Other Information: DOI: 10.1007/s00245-009-9070-4; Copyright (c) 2010 Springer Science+Business Media, LLC; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CONTROL THEORY
MARKOV PROCESS
PULSES
RANDOMNESS
VARIATIONAL METHODS
CALCULATION METHODS
STOCHASTIC PROCESSES