Cookies?
Library Header Image
LSE Research Online LSE Library Services

A zero-sum game between a singular stochastic controller and a discretionary stopper

Hernandez-Hernandez, Daniel, Simon, Robert and Zervos, Mihail (2013) A zero-sum game between a singular stochastic controller and a discretionary stopper. Annals of Applied Probability . ISSN 1050-5164 (In Press)

Full text not available from this repository.

Abstract

We consider a stochastic differential equation that is controlled by means of an additive �nite-variation process. A singular stochastic controller, who is a minimiser, determines this infinite-variation process while a discretionary stopper, who is a maximiser, 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 penalise control effort expenditure. We derive a set of variational inequalities that can fully characterise 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 C1. The non-uniqueness of the optimal strategy is an interesting feature of the game in which the controller has the first-move advantage.

Item Type: Article
Official URL: http://imstat.org/aap/
Additional Information: © 2013 IMS
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 14 Nov 2013 14:45
URL: http://eprints.lse.ac.uk/54343/

Actions (login required)

Record administration - authorised staff only Record administration - authorised staff only