A Dynkin game under Knightian uncertainty | Zendy

Hyeng Keun Koo | Zendy; Shanjian Tang | Zendy; Zhou Yang | Zendy

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A Dynkin game under Knightian uncertainty

Author(s) -

Hyeng Keun Koo,

Shanjian Tang,

Zhou Yang

Publication year - 2015

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2015.35.5467

Subject(s) - knightian uncertainty , mathematics , uniqueness , fixed point theorem , order (exchange) , pure mathematics , fixed point , banach fixed point theorem , mathematical economics , zero (linguistics) , mathematical analysis , computer science , finance , economics , linguistics , philosophy , ambiguity , programming language

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 Ito-Kunita-Wentzell formula developed by Yang and Tang (2013).

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