Robustness and Ambiguity Aversion in General Equilibrium

Abstract

We analyze the empirical predictions arising from settings of ambiguity aversion in intertemporal heterogenous agents economies. We study equilibria for two tractable wealth-homothetic settings of ambiguity aversion in continuous time. Such settings are motivated by a different robust control optimization problem. We show that ambiguity aversion affects optimal portfolio exposures in a way that is similar to an increase in risk aversion. A distinct property of the second of our settings of ambiguity aversion is that such increase is state-dependent and highly pronounced at moderate portfolio exposures. This feature causes quite prudent levels of equity market participation over a nontrivial set of states of the economy. In general equilibrium, ambiguity aversion tends to induce a higher equilibrium equity premium and lower interest rates. A distinct feature of the second of our settings of ambiguity aversion is that the equity premium part due to ambiguity aversion dominates when the exogenous random factors in the economy have low volatility. Thus, such setting can account for some distinct empirical predictions -like a limited equity market participation and ambiguity equity premia that dominate equity premia for small equity volatilities -which are unavailable under the first of our settings of ambiguity aversion.

The price of risk and ambiguity in an intertemporal general equilibrium model of asset prices

“…4 We will build mostly on the work of Trojani and Vanini (2004) and Gagliardini et al (2009). Other contributions to understanding the effects of ambiguity in general equilibrium settings are the seminal works of Dow and Werlang (1992) and Epstein and Wang (1994), and the more recent works of Correia-da-Silva and Hervés-Beloso (2009), de Castro et al (2011) and Ozsoylev and Werner (2011).…”

“…Moreover, the bound (6) constrains both the instantaneous time variation and the continuation value of the relative entropy between the reference belief, P, and any admissible contaminated belief, P h . Trojani and Vanini (2004) explain that the set h : h h ∈ [0 , 2η] , ∀t 0 defines a rectangular set of priors because any process h (and therefore any probability measure P h ) in this set corresponds to a selection of transition densities from t to t + dt, t 0 , such that h h ∈ [0 , 2η]. The fact that the specification of the ambiguity aversion is based on a rectangular set of priors guarantees a dynamically consistent preference ordering, and can be interpreted as a continuous time version of Epstein and Schneider (2003) Recursive Multiple Priors Utility.…”

Ambiguity and Time-Varying Risk Aversion in Sovereign Debt Markets

“…Hansen et al (1999) show that decision rules of investors with a requirement for robustness are observational equivalent to those of investors with higher levels of risk aversion. Maenhout (2004) and Trojani and Vanini (2004) extend on this result and document that ambiguity aversion leads to state dependence or environment-specific effective risk aversion. We build on this strand of literature that established the result that ambiguity aversion affect decision rules and relative risk aversion.…”

“…A related finding was presented in Trojani and Vanini (2004) and Maenhout (2004) for the case of robust control preferences, but without a comparative static analysis for different levels of realized ambiguity. Such exogenous changes in ambiguity are typically not accommodated by the robust control framework.…”

Robust Consumption-Investment Problem on Infinite Horizon

“…A variety of modifications to our issue were considered among others by Anderson et al [1], Faria et al [4], Gagliardini et al [9], Hansen et al [11], Trojani et al [19,20]. Most of these works consider usually the problem from an economical/financial point of view only.…”