WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 20, 2025
A Homing Problem for a Geometric Brownian Motion and Its Integral
Author:
Abstract: Let {Y (t), t ≥ 0} be a controlled geometric Brownian motion and X(t) be the integral of Y (t). The
problem of minimizing the expected time that the ratio X(t)/Y (t) will spend between two constants is considered.
The optimal control is obtained explicitly in terms of special functions. A risk-sensitive version of the cost criterion
is also proposed.