A homing problem for diffusion processes with control-dependent variance

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

2004-05-14

arxiv.org/abs/math/0405286v1

Annals of Applied Probability 2004, Vol. 14, No. 2, 786-795

Mathematics

Probability

Scientific paper

10.1214/105051604000000107

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.

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