| Optimal variational principle for backward stochastic control systems associated with Lévy processes |
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| 基金项目： | supported by National Natural Science Foundation of China (Grant No. 11101090, 11101140, 10771122);Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090071120002);Innovation Team Foundation of the Department of Education of Zhejiang Province (Grant No. T200924);Natural Science Foundation of Zhejiang Province (Grant No. Y6110775, Y6110789);Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry |
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| 摘 要： | The paper is concerned with optimal control of backward stochastic differential equation (BSDE) driven by Teugel’s martingales and an independent multi-dimensional Brownian motion,where Teugel’s martin- gales are a family of pairwise strongly orthonormal martingales associated with Lévy processes (see e.g.,Nualart and Schoutens’ paper in 2000).We derive the necessary and sufficient conditions for the existence of the op- timal control by means of convex variation methods and duality techniques.As an application,the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria (or backward linear-quadratic problem,or BLQ problem for short) is discussed and characterized by a stochastic Hamilton system.
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| 关 键 词： | stochastic control stochastic maximum principle Lévy processes Teugel’s martingales backward stochastic differential equations |
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