Large deviations for systems driven by two-time-scale nonhomogeneous Markovian chains and applications to optimal control problems

2012 ◽  
Author(s):  
Q. He ◽  
G. Yin ◽  
Q. Zhang
Keyword(s):  
Optimal Control ◽  
Large Deviations ◽  
Time Scale ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Markovian Chains

Hamilton-Jacobi Equations with Semilinear Costs and State Constraints, with Applications to Large Deviations in Games

2021 ◽  
Author(s):  
William H. Sandholm ◽  
Hung V. Tran ◽  
Srinivas Arigapudi
Keyword(s):  
Game Theory ◽  
Optimal Control ◽  
Large Deviations ◽  
Evolutionary Game Theory ◽  
State Constraints ◽  
Optimal Control Problems ◽  
Evolutionary Game ◽  
Control Problems ◽  
Optimal Solutions ◽  
Jacobi Equations

We characterize solutions of a class of time-homogeneous optimal control problems with semilinear running costs and state constraints as maximal viscosity subsolutions to Hamilton-Jacobi equations and show that optimal solutions to these problems can be constructed explicitly. We present applications to large deviations problems arising in evolutionary game theory.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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