An optimal control problem for a Wiener process with random infinitesimal mean

Mario Lefebvre, Abderrazak Moutassim


We consider a stochastic optimal control problem for one-dimensional diffusion processes with random infinitesimal mean and variance that depend on a continuoustime Markov chain. The process is controlled until it reaches either end of an interval. The aim is to minimize the expected value of a cost criterion with quadratic control costs on the way and a final cost. A particular case with a Wiener process will be treated in detail. Approximate and numerical solutions will be presented.


Homing problem; Kolmogorov backward equation; similarity solution; Brownian motion

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Copyright (c) 2019 Mario Lefebvre, Abderrazak Moutassim

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