Optimal control of nonzero sum game mean‐field delayed Markov regime‐switching forward‐backward system with Lévy processes. (14th September 2020)

• Record Type: Journal Article
• Authors: Deepa, R.; Muthukumar, P.; Hafayed, Mokhtar
• Is Part Of: Optimal control applications and methods. Volume 42:Number 1(2021)
• Page Start: 110
• Page End: 125
• Publication Date: 2020-09-14
• Subjects: infinite‐horizon -- mean‐field -- Nash equilibrium -- optimal control -- regime‐switching -- Teugels martingales; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2665
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: This article investigates the optimal control problem of nonzero sum game mean‐field delayed Markov regime‐switching forward‐backward stochastic system with Lévy processes associated with Teugels martingales over the infinite time horizon. Based on the transversality conditions, assumption of convex control domain, infinite‐horizon version of stochastic maximum principle (Nash equilibrium), and necessary condition for optimality are established. Finally, the Nash equilibrium for the optimization problem in the financial market is considered to illustrate the observed theoretical results.