The Annals of Applied Probability

A homing problem for diffusion processes with control-dependent variance

Mario Lefebvre

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Abstract

Controlled one-dimensional diffusion processes, with infinitesimal variance (instead of the infinitesimal mean) depending on the control variable, are considered in an interval located on the positive half-line. The process is controlled until it reaches either end of the interval. The aim is to minimize the expected value of a cost criterion with quadratic control costs on the way and a final cost equal to zero (resp. a large constant) if the process exits the interval through its left (resp. right) end point. Explicit expressions are obtained both for the optimal value of the control variable and the value function when the infinitesimal parameters of the processes are proportional to a power of the state variable.

Article information

Source
Ann. Appl. Probab. Volume 14, Number 2 (2004), 786-795.

Dates
First available in Project Euclid: 23 April 2004

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1082737111

Digital Object Identifier
doi:10.1214/105051604000000107

Mathematical Reviews number (MathSciNet)
MR2052902

Zentralblatt MATH identifier
02100754

Subjects
Primary: 93E20: Optimal stochastic control
Secondary: 60J60: Diffusion processes [See also 58J65]

Keywords
Dynamic programming equation stochastic differential equation hitting place Brownian motion

Citation

Lefebvre, Mario. A homing problem for diffusion processes with control-dependent variance. Ann. Appl. Probab. 14 (2004), no. 2, 786--795. doi:10.1214/105051604000000107. http://projecteuclid.org/euclid.aoap/1082737111.


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References

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