Markovian-Switching Systems: Backward and Forward-Backward Stochastic Differential Equations, Mean-Field Interactions, and Nonzero-Sum Differential Games
Esteban J. Rolón Gutiérrez, Son Luu Nguyen, George Yin
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引用次数: 0
Abstract
This work is devoted to Markovian-switching systems. In particular, backward stochastic differential equations (BSDEs), forward-backward stochastic differential equations (FBSDEs), such equations with mean-field interactions, and related nonzero-sum stochastic mean-field games. First, BSDEs with Markovian switching, FBSDEs with Markovian-switching, and FBSDEs with both mean-field interactions and regime-switching are examined. Unique solvability of the underlying equations is obtained under monotonicity conditions without assuming non-degeneracy condition for the forward equation. Then the existence of open-loop Nash equilibrium points for nonzero-sum linear-quadratic stochastic differential games with random coefficients is investigated.
期刊介绍：
The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.
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