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Optimal control of nonzero sum game mean‐field delayed Markov regime‐switching forward‐backward system with Lévy processes
Author(s) -
Deepa R.,
Muthukumar P.,
Hafayed Mokhtar
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2665
Subject(s) - transversality , nash equilibrium , mathematics , optimal control , markov chain , stochastic control , maximum principle , regular polygon , markov process , mathematical optimization , mathematical economics , mean field theory , mathematical analysis , physics , statistics , quantum mechanics , geometry
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.