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July/August 2009 Uniqueness for nonlinear parabolic systems in stochastic game theory with application to financial economics
Carsten Ebmeyer, Jens Vogelgesang
Differential Integral Equations 22(7/8): 601-615 (July/August 2009).

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.

Citation

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Carsten Ebmeyer. Jens Vogelgesang. "Uniqueness for nonlinear parabolic systems in stochastic game theory with application to financial economics." Differential Integral Equations 22 (7/8) 601 - 615, July/August 2009.

Information

Published: July/August 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35237
MathSciNet: MR2532113

Subjects:
Primary: 35K51
Secondary: 35A02, 91A15

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.22 • No. 7/8 • July/August 2009
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