|Publication ahead of print|
|Published online||21 June 2017|
Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problems∗
School of Mathematics, Shandong University, Jinan 250100, P.R. China.
Received: 5 November 2015
Revised: 24 July 2016
Accepted: 3 August 2016
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.
Mathematics Subject Classification: 60H10 / 93E20 / 49N10
Key words: Forward-backward stochastic differential equation / monotonicity condition / stochastic optimal control / nonzero-sum stochastic differential game / linear-quadratic problem
© EDP Sciences, SMAI 2017
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