Abstract
This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps. The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations. The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed. All these results develop those of Lim, Zhou (2001) and Yu, Ji (2008).
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This research is supported by National Natural Science Foundation of China (10671112), National Basic Research Program of China (973 Program) (2007CB814904) and the Natural Science Foundation of Shandong Province (Z2006A01).
This paper was recommended for publication by Editor Jifeng ZHANG.
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Zhang, D. Backward linear-quadratic stochastic optimal control and nonzero-sum differential game problem with random jumps. J Syst Sci Complex 24, 647–662 (2011). https://doi.org/10.1007/s11424-010-8365-5
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DOI: https://doi.org/10.1007/s11424-010-8365-5