  We treat the exterior Dirichlet problem for a class of fully nonlinear
elliptic equations of the form $$f(\lambda(D^2u))=g(x),$$ with prescribed
asymptotic behavior at infinity. The equations of this type had been studied
extensively by Caffarelli--Nirenberg--Spruck \cite{Caffarelli1985}, Trudinger
\cite{Trudinger1995} and many others, and there had been significant
discussions on the solvability of the classical Dirichlet problem via the
continuity method, under the assumption that $f$ is a concave function. In this
paper, based on the Perron's method, we establish an exterior existence and
uniqueness result for viscosity solutions of the equations by assuming $f$ to
satisfy certain structure conditions as in \cite{Caffarelli1985,Trudinger1995},
which may embrace the well-known Monge--Amp\`ere equations, Hessian equations
and Hessian quotient equations as special cases but do not require the
concavity.
