A Dynkin game under Knightian uncertainty

Hyeng Keun  Koo; Shanjian  Tang; Zhou  Yang

doi:10.3934/dcds.2015.35.5467

Article Contents

2015, Volume 35, Issue 11: 5467-5498. Doi: 10.3934/dcds.2015.35.5467

This issue Previous Article Switching game of backward stochastic differential equations and associated system of obliquely reflected backward stochastic differential equations Next Article A stochastic maximum principle with dissipativity conditions

A Dynkin game under Knightian uncertainty

1.
Graduate Department of Financial Engineering, Ajou University, Suwon 443-749
2.
School of Mathematical Science, Fudan University, Shanghai 200433
3.
School of Mathematical Science, South China Normal University, Guangzhou 510631

Received: October 31, 2012

Revised: September 30, 2014

Published: October 2015

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Abstract

We study a zero-sum Dynkin game under Knghtian uncertainty. The associated Hamiton-Jacobi-Bellman-Isaacs equation takes the form of a semi-linear backward stochastic partial differential variational inequality (SBSPDVI). We establish existence and uniqueness of a strong solution by using the Banach fixed point theorem and a comparison theorem. A solution to the SBSPDVI is used to construct a saddle point of the Dynkin game. In order to establish this verification we use the generalized Itó-Kunita-Wentzell formula developed by Yang and Tang (2013).

Keywords:

Backward stochastic partial differential equation,
variational inequality,
Dynkin game,
super-parabolicity.

Mathematics Subject Classification: 93E20, 93E03, 49L20, 60H15, 35R60, 34F05.

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