This paper investigates the near-optimality for a class of forward-backward stochastic differential equations (FBSDEs) with continuous-time finite state Markov chains. The control domains are not necessarily convex and the control variables do not enter forward diffusion term. Some new estimates for state and adjoint processes arise naturally when we consider the near-optimal control problem in the framework of regime-switching. Inspired by Ekeland’s variational principle and a spike variational technique, the necessary conditions are derived, which imply the near-minimum condition of the Hamiltonian function in an integral sense. Meanwhile, some certain convexity conditions and the near-minimum condition are sufficient for the near-optimal controls with order $$. A recursive utility investment consumption problem is discussed to illustrate the effectiveness of our theoretical results.
Mots-clés : Forward-backward stochastic differential equation, regime-switching, near-optimality, Ekeland’s variational principle, necessary conditions, sufficient conditions
@article{COCV_2020__26_1_A94_0, author = {Li, Min and Wu, Zhen}, title = {Near-optimal control problems for forward-backward regime-switching systems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {26}, year = {2020}, doi = {10.1051/cocv/2020016}, mrnumber = {4175375}, zbl = {1460.93110}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2020016/} }
TY - JOUR AU - Li, Min AU - Wu, Zhen TI - Near-optimal control problems for forward-backward regime-switching systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2020016/ DO - 10.1051/cocv/2020016 LA - en ID - COCV_2020__26_1_A94_0 ER -
%0 Journal Article %A Li, Min %A Wu, Zhen %T Near-optimal control problems for forward-backward regime-switching systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2020016/ %R 10.1051/cocv/2020016 %G en %F COCV_2020__26_1_A94_0
Li, Min; Wu, Zhen. Near-optimal control problems for forward-backward regime-switching systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 94. doi : 10.1051/cocv/2020016. http://www.numdam.org/articles/10.1051/cocv/2020016/
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This work was supported by the National Natural Science Foundation of China (11831010,61961160732), and Shandong Provincial Natural Science Foundation (ZR2019ZD42).