A necessary condition for mean-field type stochastic differential equations with correlated state and observation noises

Haiyan  Zhang

doi:10.3934/jimo.2016.12.1287

Article Contents

2016, Volume 12, Issue 4: 1287-1301. Doi: 10.3934/jimo.2016.12.1287

This issue Previous Article Stability analysis of a delayed social epidemics model with general contact rate and its optimal control Next Article Semicontinuity of approximate solution mappings to generalized vector equilibrium problems

A necessary condition for mean-field type stochastic differential equations with correlated state and observation noises

Haiyan Zhang^1,

1.
College of Sciences, Shandong Jiaotong University, Jinan 250023

Received: February 28, 2015

Revised: May 31, 2015

Published: September 2016

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Abstract

This paper is concerned with a mean-field type optimal control problem, whose new features are that the state $x^v_t$ is partially observed by a noisy process $y(t)$, and the control problem is time inconsistent in the sense that Bellman optimality principle does not work. A necessary condition for optimality is derived by convex variation, dual technique and backward stochastic differential equations (BSDEs). A linear-quadratic (LQ) optimal control example is studied, and the optimal solution is obtained by the optimal filtering for BSDEs and the necessary condition.

Keywords:

Mean-field control,
correlated state and observation noises,
necessary condition,
LQ control,
filtering.

Mathematics Subject Classification: Primary: 93E11, 93E20; Secondary: 60H10.

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