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On stochastic optimal control laws

Published online by Cambridge University Press:  22 January 2016

Makiko Nisio
Makiko Nisio*
Affiliation:
Kobe University
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Let us begin by recalling the existence of optimal controls for a class of stochastic differential equations

with given initial condition X(0) = x, where B is an n-dimensional Brownian motion and the control U is a stochastic process. As admissible controls, let us allow all non-anticipative process U(t) = (U1(t),…Um(t)) ∈ Γ where Γ is a compact subset of Rm. We call Γ a control region. Assume that the matrix valued functional β and the n-vector valued α satisfy a Lipscitz condition in X and some growth condition. Then we have a unique solution Xu for an admissible control U.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 52 , December 1973 , pp. 1 - 30
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

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