Mario Lefebvre, "A Homing Problem for a Geometric Brownian Motion and Its Integral," WSEAS Transactions on Systems and Control, vol. 20, pp. 9-12, 2025, DOI:10.37394/23203.2025.20.2
Mario Lefebvre. A Homing Problem for a Geometric Brownian Motion and Its Integral.
WSEAS Transactions on Systems and Control. 2025;20:9-12. 10.37394/23203.2025.20.2
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.
Keywords:
Stochastic optimal control, first-passage time, dynamic programming, special functions, risk-sensitivity
Pages: 9-12 WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 20, 2025, Art. #2 DOI: 10.37394/23203.2025.20.2
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