Two Approaches to Non-Zero-Sum Stochastic Differential Games of Control and Stopping

Two Approaches to Non-Zero-Sum Stochastic Dif ...
Qinghua Li, Qinghua Li
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Last edited by MARC Bot
December 21, 2022 | History

Two Approaches to Non-Zero-Sum Stochastic Differential Games of Control and Stopping

This dissertation takes two approaches - martingale and backward stochastic differential equation (BSDE) - to solve non-zero-sum stochastic differential games in which all players can control and stop the reward streams of the games. Existence of equilibrium stopping rules is proved under some assumptions. The martingale part provides an equivalent martingale characterization of Nash equilibrium strategies of the games. When using equilibrium stopping rules, Isaacs' condition is necessary and sufficient for the existence of an equilibrium control set. The BSDE part shows that solutions to BSDEs provide value processes of the games. A multidimensional BSDE with reflecting barrier is studied in two cases for its solution: existence and uniqueness with Lipschitz growth, and existence in a Markovian system with linear growth rate.

Publish Date
Language
English

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Edition Notes

Department: Statistics.

Thesis advisor: Ioannis Karatzas.

Thesis (Ph.D.)--Columbia University, 2011.

Published in
[New York, N.Y.?]

The Physical Object

Pagination
1 online resource.

Edition Identifiers

Open Library
OL44629309M
OCLC/WorldCat
867753580

Work Identifiers

Work ID
OL32804813W

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marc_columbia MARC record

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December 21, 2022 Created by MARC Bot Imported from marc_columbia MARC record