## Differential and Integral Equations

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

#### 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

https://projecteuclid.org/euclid.die/1356019540

Mathematical Reviews number (MathSciNet)
MR2532113

Zentralblatt MATH identifier
1240.35237

#### 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