Abstract
We study the existence and uniqueness of the following kind of backward stochastic differential equation,
under local Lipschitz condition, where (Ω, ℱ,P, W(·), ℱt) is a standard Wiener process, for any given (x, y),f(x, y, ·) is an ℱt-adapted process, andX is ℱt-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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Communicated by D. Ocone
This work was partially supported by the Chinese National Natural Science Foundation and SEDC Foundation for Young Academics.
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Peng, S. Backward stochastic differential equations and applications to optimal control. Appl Math Optim 27, 125–144 (1993). https://doi.org/10.1007/BF01195978
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DOI: https://doi.org/10.1007/BF01195978
Key words
- Backward stochastic differential equations
- Controlled diffusion processes
- Stochastic maximum principle
- Matrix-valued random Riccati equations