Linear-quadratic control of backward stochastic differential equations (Q2753213)
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scientific article; zbMATH DE number 1667490
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Linear-quadratic control of backward stochastic differential equations |
scientific article; zbMATH DE number 1667490 |
Statements
29 October 2001
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backward stochastic differential equations
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linear-quadratic optimal control
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Riccati equations
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completion of squares
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constrained optimization
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Linear-quadratic control of backward stochastic differential equations (English)
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The optimal control for the backward linear-quadratic control problem is derived explicitly in terms of a pair of Riccati equations, a forward stochastic differential equation, and a backward stochastic differential equation. It is shown that this optimal control coincides with the solution to a constrained forward linear-quadratic problem and is the limiting solution to a family of unconstrained forward linear-quadratic problems. A proof of the existence and uniqueness of solutions of the above mentioned Riccati equations is obtained. The case of random coefficients is discussed.
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