## The Annals of Applied Probability

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

### A homing problem for diffusion processes with control-dependent variance

#### 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**

https://projecteuclid.org/euclid.aoap/1082737111

**Digital Object Identifier**

doi:10.1214/105051604000000107

**Mathematical Reviews number (MathSciNet)**

MR2052902

**Zentralblatt MATH identifier**

1061.93099

**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. https://projecteuclid.org/euclid.aoap/1082737111