A Note on Costs Minimization with Stochastic Target Constraints
Probability
2020-01-28 v3
Abstract
We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order semi--linear ordinary differential equation (ODE). Moreover, we establish the optimal control. In the second example we show that the case of exponential costs leads to a trivial optimal control.
Cite
@article{arxiv.1907.02429,
title = {A Note on Costs Minimization with Stochastic Target Constraints},
author = {Yan Dolinsky and Benjamin Gottesman and Ori Gurel-Gurevich},
journal= {arXiv preprint arXiv:1907.02429},
year = {2020}
}
Comments
13 pages, 3 figures