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
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. https://doi.org/10.57262/die/1356019540
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