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

Mario Lefebvre

Stochastic Processes and their Applications, 1997, vol. 69, issue 1, 71-82

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.

Keywords: Stochastic; optimal; control; Homing; problem; Riccati; equation; Hitting; time (search for similar items in EconPapers)
Date: 1997
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