Optimality of two-parameter strategies in stochastic control
Optimization and Control
2016-05-18 v1 Probability
Mathematical Finance
Abstract
In this note, we study a class of stochastic control problems where the optimal strategies are described by two parameters. These include a subset of singular control, impulse control, and two-player stochastic games. The parameters are first chosen by the two continuous/smooth fit conditions, and then the optimality of the corresponding strategy is shown by verification arguments. Under the setting driven by a spectrally one-sided Levy process, these procedures can be efficiently done thanks to the recent developments of scale functions. In this note, we illustrate these techniques using several examples where the optimal strategy as well as the value function can be concisely expressed via scale functions.
Cite
@article{arxiv.1605.04995,
title = {Optimality of two-parameter strategies in stochastic control},
author = {Kazutoshi Yamazaki},
journal= {arXiv preprint arXiv:1605.04995},
year = {2016}
}