Existence and uniqueness of viscosity solutions to the exterior problem of a parabolic Monge-Ampère equation

In this paper, we use the Perron method to prove the existence and uniqueness of the exterior problem for a kind of parabolic Monge-Ampere equation \begin{document}$ -u_t+\log\det D^2u = f(x) $\end{document} with prescribed asymptotic behavior at infinity, where \begin{document}$ f $\end{document} is asymptotically close to a radial function at infinity. We generalize the results of both the elliptic exterior problems and the parabolic interior problems for the Monge-Ampere equations.