On Dynamic Programming Principle for Stochastic Control under Expectation Constraints
arXiv:1802.03954
Abstract
This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical space at each time t. Motivated by some financial applications, we show that several types of dynamic trading constraints can be reformulated into expectation constraints on paths of controlled state processes. Our results can therefore be employed to recover the dynamic programming principle for these optimal investment problems under dynamic constraints, possibly path-dependent, in a non-Markovian framework.
arXiv commentFinal version, to appear in Journal of Optimization Theory and Applications. Keywords: Dynamic programming principle, Measurable selection, Intermediate expectation constraints, Dynamic trading constraints
References in corpus (4)
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- Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems
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- Dynamic Programming Principles for Optimal Stopping with Expectation Constraint