Backward stochastic differential equations and applications to optimal control |
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Authors: | Shige Peng |
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Institution: | 1. Department of Mathematics, Shandong University, 250100, Jinan, Shandong, People's Republic of China
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Abstract: | We study the existence and uniqueness of the following kind of backward stochastic differential equation, $$x(t) + \int_t^T {f(x(s),y(s),s)ds + \int_t^T {y(s)dW(s) = X,} }$$ under local Lipschitz condition, where (Ω, ?,P, W(·), ?t) is a standard Wiener process, for any given (x, y),f(x, y, ·) is an ?t-adapted process, andX is ?t-measurable. The problem is to look for an adapted pair (x(·),y(·)) that solves the above equation. A generalized matrix Riccati equation of that type is also investigated. A new form of stochastic maximum principle is obtained. |
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