Accounting for Risk in a Linearized Solution: How to Approximate the Risky Steady State and Around It

We propose a novel approximation of the risky steady state and construct first-order perturbations around it for general class dynamic equilibrium models with time-varying non-Gaussian risk. offer analytical formulas conditions their local existence uniqueness. apply this technique to featuring Campbell-Cochrane habits, recursive preferences, disaster risk, show how proposed represents implications model similarly global solution methods. that our cannot be generically replicated by higher-order deterministic state, which account well effects risk in applications even up third order. Finally, we argue perturbation can viewed as generalized version heuristic loglinear-lognormal approximations commonly used macro-finance literature.