ALTERNATIVE THEORETICAL FRAMEWORKS FOR FINITE HORIZON DISCRETE-TIME STOCHASTIC OPTIMAL CONTROL.

Steven E. Shreve, Dimitri P. Bertsekas

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

Stochastic optimal control problems are usually analyzed under one of three types of assumptions: (a) Countability assumptions on the underlying probability space - this eliminates all difficulties of measure theoretic nature; (b) Semicontinuity assumptions under which the existence of optimal Borel measurable policies can be guaranteed; and (c) Borel measurability assumptions under which the existence of p-optimal or p- epsilon -optimal Borel measurable policies can be guaranteed. A general theoretical framework based on outer integration is introduced which contains these three models as special cases. Within this framework all known results for finite horizon problems together with some new ones are proved and subsequently specialized. An important new feature of specialization to the Borel measurable model is the introduction of universally measurable policies. It is shown that everywhere optimal or nearly optimal policies exist within this class and this enables one to dispense with the notion of p-optimality.

Original languageEnglish (US)
Pages (from-to)953-978
Number of pages26
JournalSIAM Journal on Control and Optimization
Volume16
Issue number6
DOIs
StatePublished - 1978
Externally publishedYes

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

Fingerprint Dive into the research topics of 'ALTERNATIVE THEORETICAL FRAMEWORKS FOR FINITE HORIZON DISCRETE-TIME STOCHASTIC OPTIMAL CONTROL.'. Together they form a unique fingerprint.

Cite this