  In this paper, we establish the existence and uniqueness theorem for
solutions of the exterior Dirichlet problem for Hessian quotient equations with
prescribed asymptotic behavior at infinity. This extends the previous related
results on the Monge-Amp\`{e}re equations and on the Hessian equations, and
rearranges them in a systematic way. Based on the Perron's method, the main
ingredient of this paper is to construct some appropriate subsolutions of the
Hessian quotient equation, which is realized by introducing some new quantities
about the elementary symmetric functions and using them to analyze the
corresponding ordinary differential equation related to the generalized
radially symmetric subsolutions of the original equation.
