Geodesic
Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problems
Yu, Zhiyong1
1 School of Mathematics, Shandong University, Jinan 250100, P.R. China
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1331-1359

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In this paper, we investigate infinite horizon jump-diffusion forward-backward stochastic differential equations under some monotonicity conditions. We establish an existence and uniqueness theorem, two stability results and a comparison theorem for solutions to such kind of equations. Then the theoretical results are applied to study a kind of infinite horizon backward stochastic linear-quadratic optimal control problems, and then differential game problems. The unique optimal controls for the control problems and the unique Nash equilibrium points for the game problems are obtained in closed forms.

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DOI : 10.1051/cocv/2016055
Classification : 60H10, 93E20, 49N10
Keywords: Forward-backward stochastic differential equation, monotonicity condition, stochastic optimal control, nonzero-sum stochastic differential game, linear-quadratic problem

Yu, Zhiyong 1

1 School of Mathematics, Shandong University, Jinan 250100, P.R. China 
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     title = {Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1331--1359},
     publisher = {EDP-Sciences},
     volume = {23},
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Yu, Zhiyong. Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1331-1359. doi: 10.1051/cocv/2016055

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