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Necessary and sufficient conditions of near‐optimality in a regime‐switching diffusion model
Author(s) -
Li Min,
Wu Zhen
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.2571
Subject(s) - mathematics , markov chain , optimal control , regular polygon , diffusion , stochastic differential equation , markov process , state (computer science) , stochastic control , maximum principle , mathematical optimization , type (biology) , diffusion process , computer science , physics , algorithm , thermodynamics , ecology , knowledge management , statistics , geometry , innovation diffusion , biology
Summary This paper is concerned with the stochastic near‐optimal control problem for a regime‐switching diffusion model, where the control domains are convex. The controlled system is described by the Itô‐type stochastic differential equation (SDE) with a continuous‐time Markov chain, which possesses a finite state structure. Some new estimates for state and adjoint processes are obtained in the presence of the Markovian jumps. Based on these estimates and Ekeland's variational principle, the necessary and sufficient conditions for near‐optimality of this model are established. A numerical example is given to illustrate the effectiveness of theoretical results.