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

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  • Lefebvre, Mario

Abstract

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.

Suggested Citation

  • Lefebvre, Mario, 1997. "Using a geometric Brownian motion to control a Brownian motion and vice versa," Stochastic Processes and their Applications, Elsevier, vol. 69(1), pages 71-82, July.
    • Handle: RePEc:eee:spapps:v:69:y:1997:i:1:p:71-82
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    References listed on IDEAS

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    1. Lefebvre, Mario, 1987. "Optimal control of an Ornstein-Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 24(1), pages 89-97, February.
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