Games of singular control and stopping driven by spectrally one-sided Lévy processes
type: Item
instance of: scholarly article
title: Games of singular control and stopping driven by spectrally one-sided Lévy processes
zbMATH Open document ID: 1319.91026
author: Daniel Hernández-Hernández
author: Kazutoshi Yamazaki
published in: Stochastic Processes and their Applications
publication date: 2014-11-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1308.3141
review text: A two-person zero-sum game is considered wherein one player controls a Lévy process with an additive singular control and the other player stops the process at a stopping time. The payoff is the sum of integral costs depending on resp. the state process and the singular control till the stopping time, plus a terminal cost. For the cases where the spectral density of the Lévy process is supported in either positive or negative half line, a Nash equilibrium is shown to exist wherein the stopping time is based on a threshold rule, whereas the optimal singular control is a reflecting barrier for the controlled process. The proof uses sufficient conditions in terms of the associated variational inequalities. Some numerical examples are given.
Mathematics Subject Classification ID: 91A15
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 91A25
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 6366967
zbMATH Keywords: stopping game
zbMATH Keywords: singular control
zbMATH Keywords: spectrally one sided Lévy process
MaRDI profile type: Publication
OpenAlex ID: W2009790812
arXiv ID: 1308.3141
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DOI: 10.1016/J.SPA.2014.07.020
description: scientific article; zbMATH DE number 6366967