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An Information-Based Approximation Scheme for Stochastic Optimization Problems in Continuous Time

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abstract Dynamic stochastic optimization problems with a large (possibly infinite) number of decision stages and high-dimensional state vectors are inherently difficult to solve. In fact, scenario tree-based algorithms are unsuitable for problems with many stages, while dynamic programming-type techniques are unsuitable for problems with many state variables. This paper proposes a stage aggregation scheme for stochastic optimization problems in continuous time, thus having an extremely large (i.e., uncountable) number of decision stages. By perturbing the underlying data and information processes, we construct two approximate problems that provide bounds on the optimal value of the original problem. Moreover, we prove that the gap between the bounds converges to zero as the stage aggregation is refined. If massive aggregation of stages is possible without sacrificing too much accuracy, the aggregate approximate problems can be addressed by means of scenario tree-based methods. The suggested approach applies to problems that exhibit randomness in the objective and the constraints, while the constraint functions are required to be additively separable in the decision variables and random parameters.
   
type journal paper
   
keywords stochastic optimization, stochastic control, bounds, time discretization, stage aggregation
   
language English
kind of paper journal article
date of appearance 1-5-2009
journal Mathematics of Operations Research
publisher INFORMS (Hanover, USA)
ISSN 0364-765X
ISSN (online) 1526-5471
volume of journal 34
number of issue 2
page(s) 428-444
review double-blind review
   
citation Kuhn, D. (2009). An Information-Based Approximation Scheme for Stochastic Optimization Problems in Continuous Time. Mathematics of Operations Research, 34(2), 428-444.