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separation theorem

   Also found in: Financial, Wikipedia 0.01 sec.
separation theorem [‚sep·ə′rā·shən ‚thir·əm]
(control systems)
A theorem in optimal control theory which states that the solution to the linear quadratic Gaussian problem separates into the optimal deterministic controller (that is, the optimal controller for the corresponding problem without noise) in which the state used is obtained as the output of an optimal state estimator.


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The separation theorem says, for instance, that there is a vector orthogonal to the point b' on the arm such that for any h in H, ph' [less than or equal to] ph, and for any b in B, pb' [greater than or equal to] pb.
We show that imperfect hedging violates both the separation theorem and the full hedging theorem.
 
 
 
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