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

The Dirichlet problem for Hessian quotient equations on exterior domains