A stochastic maximum principle for risk-sensitive mean-field-type control

Boualem Djehiche, Tembine Hamidou, Raul Tempone

Research output: Contribution to journalConference article

Abstract

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle for optimal control of stochastic differential equations of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. For a general action space a Peng's type stochastic maximum principle is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type under linear stochastic dynamics with exponential quadratic cost function. Explicit characterizations are given for both mean-field free and mean-field risk-sensitive models.

Original languageEnglish (US)
Article number7039929
Pages (from-to)3481-3486
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume2015-February
Issue numberFebruary
DOIs
StatePublished - Jan 1 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

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ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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