Limit Theorem for Controlled Backward SDEs and Homogenization of Hamilton-Jacobi-Bellman Equations
- Departement de Mathematiques, Universite de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu, B.P. 809, 29285 Brest Cedex (France)
We prove a convergence theorem for a family of value functions associated with stochastic control problems whose cost functions are defined by backward stochastic differential equations. The limit function is characterized as a viscosity solution to a fully nonlinear partial differential equation of second order. The key assumption we use in our approach is shown to be a necessary and sufficient assumption for the homogenizability of the control problem. The results generalize partially homogenization problems for Hamilton-Jacobi-Bellman equations treated recently by Alvarez and Bardi by viscosity solution methods. In contrast to their approach, we use mainly probabilistic arguments, and discuss a stochastic control interpretation for the limit equation.
- OSTI ID:
- 21064220
- Journal Information:
- Applied Mathematics and Optimization, Vol. 51, Issue 1; Other Information: DOI: 10.1007/s00245-004-0805-3; Copyright (c) 2005 Springer Science+Business Media, Inc.; Article Copyright (c) 2004 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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