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Using a geometric Brownian motion to control a Brownian motion and vice versa

Let x(t) be a one-dimensional Brownian motion. The homing problem for a controlled x(t) process is solved by using a mathematical expectation for an uncontrolled geometric Brownian motion. Furthermore, it turns out that the optimally controlled process is a Bessel process. Similarly, a geometric Brownian motion is optimally controlled by using a mathematical expectation for an uncontrolled Brownian motion process.
Year of publication:
1997
Authors: Lefebvre, Mario
Published in:
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 69.1997, 1, p. 71-82
Publisher: Elsevier
Keywords: Stochastic optimal control Homing problem Riccati equation Hitting time
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Type of publication: Article
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Persistent link: https://www.econbiz.de/10008874741
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