Geodesic
Stochastic optimal control problem with infinite horizon driven by G-Brownian motion
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 873-899

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The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the unique viscosity solution of the related Hamilton−Jacobi−Bellman−Isaacs (HJBI) equation.

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DOI : 10.1051/cocv/2017044
Classification : 93E20, 60H10, 35J60
Keywords: G-Brownian motion, backward stochastic differential equations, stochastic optimal control, dynamic programming principle

Hu, Mingshang 1 ; Wang, Falei 1

1 
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     author = {Hu, Mingshang and Wang, Falei},
     title = {Stochastic optimal control problem with infinite horizon driven by {G-Brownian} motion},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {873--899},
     publisher = {EDP-Sciences},
     volume = {24},
     number = {2},
     year = {2018},
     doi = {10.1051/cocv/2017044},
     mrnumber = {3816420},
     zbl = {1401.93224},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017044/}
}
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Hu, Mingshang; Wang, Falei. Stochastic optimal control problem with infinite horizon driven by G-Brownian motion. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 873-899. doi: 10.1051/cocv/2017044

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