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October  2016, 12(4): 1287-1301. doi: 10.3934/jimo.2016.12.1287

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

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

Received  March 2015 Revised  June 2015 Published  January 2016

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.
Citation: Haiyan Zhang. A necessary condition for mean-field type stochastic differential equations with correlated state and observation noises. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1287-1301. doi: 10.3934/jimo.2016.12.1287
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