151. Weak Dynamic Programming for Generalized State Constraints
- Author
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Marcel Nutz, Bruno Bouchard, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Centre de Recherche en Économie et Statistique (CREST), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris)-Centre National de la Recherche Scientifique (CNRS), and Department of Mathematics
- Subjects
Comparison theorem ,0209 industrial biotechnology ,Control and Optimization ,Viscosity solution ,MathematicsofComputing_NUMERICALANALYSIS ,Hamilton–Jacobi–Bellman equation ,Systems and Control (eess.SY) ,02 engineering and technology ,Weak formulation ,01 natural sciences ,FOS: Economics and business ,Mathematics - Analysis of PDEs ,020901 industrial engineering & automation ,AMS 2000 Subject Classifications:93E20,49L20,49L25,35K55 ,FOS: Mathematics ,FOS: Electrical engineering, electronic engineering, information engineering ,Applied mathematics ,0101 mathematics ,Mathematics - Optimization and Control ,Mathematics ,Stochastic control ,Expectation constraint ,Applied Mathematics ,Probability (math.PR) ,010102 general mathematics ,State (functional analysis) ,93E20, 49L20, 49L25, 35K55 ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,Dynamic programming ,Optimization and Control (math.OC) ,Risk Management (q-fin.RM) ,Computer Science - Systems and Control ,Relaxation (approximation) ,Weak dynamic programming ,State constraint ,Hamilton-Jacobi-Bellman equation ,Mathematics - Probability ,Analysis of PDEs (math.AP) ,Quantitative Finance - Risk Management - Abstract
We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the viscosity sense. We treat open state constraints as a special case of expectation constraints and prove a comparison theorem to obtain the equation for closed state constraints., 36 pages;forthcoming in 'SIAM Journal on Control and Optimization'
- Published
- 2012