  In this paper, we consider the exterior Dirichlet problem for Hessian
quotient equations with the right hand side $g$, where $g$ is a positive
function and $g=1+O(|x|^{-\beta})$ near infinity, for some $\beta>2$. Under a
prescribed generalized symmetric asymptotic behavior at infinity, we establish
an existence and uniqueness theorem for viscosity solutions, by using
comparison principles and Perron's method. This extends the previous results
for Monge--Amp\`ere equations and Hessian equations.
