A ZERO-SUM GAME BETWEEN A SINGULAR STOCHASTIC CONTROLLER AND A DISCRETIONARY STOPPER
成果类型：
Article
署名作者：
Hernandez-Hernandez, Daniel; Simon, Robert S.; Zervos, Mihail
署名单位：
CIMAT - Centro de Investigacion en Matematicas; University of London; London School Economics & Political Science
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/13-AAP986
发表日期：
2015
页码：
46-80
关键词：
摘要：
We consider a stochastic differential equation that is controlled by means of an additive finite-variation process. A singular stochastic controller, who is a minimizer, determines this finite-variation process, while a discretionary stopper, who is a maximizer, chooses a stopping time at which the game terminates. We consider two closely related games that are differentiated by whether the controller or the stopper has a first-move advantage. The games' performance indices involve a running payoff as well as a terminal payoff and penalize control effort expenditure. We derive a set of variational inequalities that can fully characterize the games' value functions as well as yield Markovian optimal strategies. In particular, we derive the explicit solutions to two special cases and we show that, in general, the games' value functions fail to be C-1. The nonuniqueness of the optimal strategy is an interesting feature of the game in which the controller has the first-move advantage.
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