Optimal variational principle for backward stochastic control systems associated with Lévy processes |
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Authors: | MaoNing Tang Qi Zhang |
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Institution: | 1. Department of Mathematical Sciences, Huzhou University, Huzhou, 313000, China 2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China
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Abstract: | 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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Keywords: | stochastic control stochastic maximum principle Lévy processes Teugel’s martingales backward stochastic differential equations |
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