Differential and Integral Equations

Uniqueness for nonlinear parabolic systems in stochastic game theory with application to financial economics

Carsten Ebmeyer and Jens Vogelgesang

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Abstract

The objective of this paper is to study nonlinear partial differential systems like $$ \partial_t {\bf u}- \Delta {\bf u} +{\bf H}(x,t,{\bf u}, \nabla {\bf u})={\bf G}(x,t), $$ with applications to the solution of stochastic differential games with $N$ players, where $N$ is arbitrarily large. It is assumed that the Hamiltonian ${\bf H}$ of the nonlinear system satisfies a quadratic growth condition in $\nabla {\bf u}$ and has a positive definite Jacobian ${\bf H_u}$. An energy estimate and the uniqueness property for bounded weak solutions are proved. Moreover, applications to stochastic games and financial economics such as modern portfolio theory are discussed.

Article information

Source
Differential Integral Equations Volume 22, Number 7/8 (2009), 601-615.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019540

Mathematical Reviews number (MathSciNet)
MR2532113

Zentralblatt MATH identifier
1240.35237

Subjects
Primary: 35K51: Initial-boundary value problems for second-order parabolic systems
Secondary: 35A02: Uniqueness problems: global uniqueness, local uniqueness, non- uniqueness 91A15: Stochastic games

Citation

Ebmeyer, Carsten; Vogelgesang, Jens. Uniqueness for nonlinear parabolic systems in stochastic game theory with application to financial economics. Differential Integral Equations 22 (2009), no. 7/8, 601--615. https://projecteuclid.org/euclid.die/1356019540.


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