Risk, Robustness and Knightian Uncertainty in Continuous-Time, Heterogenous Agents, Financial Equilibria

Abstract

We analyze and compare analytically continuous-time financial equilibria where heterogeneous risk averse investors care about model misspecification through some preference for robustness and in the presence of a stochastic opportunity set. This incorporates a concern for model misspecification into equilibrium asset prices. Since no exact equilibrium computations are possible in this model setting, perturbation theory is used to provide first order asymptotics for the implied equilibria. We find that to first order robustness enhances eective risk aversion while keeping constant the preference for intertemporal substitution. Therefore, equilibrium consumption, equilibrium capital stock dynamics (in production economies) and equilibrium stock price processes (in exchange economies) are not directly modified by a preference for robustness. By contrast, robustness aects directly optimal portfolios, causing lower equilibrium interest rates - and thereby enhanced risk premia - when the speculative investment motive dominates the intertem-poral hedging demand. Finally, at variance with other robustness specifications, definitions of robustness that mimic Knightian uncertainty produce state dependent eective risk aversions that generate first order risk aversion eects on optimal portfolios, equilibrium interest rates and equity premia. This yields functional forms for some key equilibrium variables like equity premia which are structurally different from those implied by standard risk aversion or other robustness definitions, which reflect all second order risk aversion. Moreover, under Knightian uncertainty the structure of an equilibrium depends strongly on the completeness of the underlying economy. For instance, within complete production economies we find that Knightian uncertainty can generate an endogenous stock market participation, a feature that cannot be obtained by the other robustness definitions. The richness of the equilibrium eects generated in our heterogenous economies suggests that definitions of robustness which mimic Knightian uncertainty can generate the largest variety of robust economic behaviours in the presence of model uncertainty.

Keywords: Financial Equilibria, Knightian Uncertainty, Model Misspecification, Perturbation Theory, Robust Decision Making

JEL Classification: C60, C61, G11