We examine the problem of an agent who faces income risk and who insures himself by accumulating holdings of a riskless bond, subject to a no-borrowing constraint. The problem is novel since the agent is concerned that his benchmark model is misspecified. We use robust control analysis to model this concern. We consider several benchmark models of income risk - a simple one-shock case, a two-shock case, and a one-shock case with the possibility of an extreme adverse realization. We characterize the `worst case' models entertained by the agent and examine how their properties inform his actions. We show that the agent's fears can be represented by processes featuring a negative mean shift in his income, increased persistence of bad income states and lower persistence of good income states. These properties are particularly pronounced in the extreme shock case. In the two shock case the worst case model exhibits positive correlations between the income components - even though no such correlation exists under the benchmark. Overall the agent fears a world in which he is driven to low levels of wealth more rapidly than in his benchmark model. This enhances his desire to accumulate wealth, from a precautionary motive. Importantly, the distortions to the conditional distributions of innovations are more pronounced when the agent's wealth level is low. Thus the pessimism of the robust agent is state dependent. Intriguingly, this opens an interesting avenue to complex feedbacks between agents' pessimism and their decisions that are, in turn, influenced by this pessimism.

We examine the asset pricing properties of an endowment economy featuring a random walk consumption process with stochastic volatility and a specication of preferences interpretable as reflecting risk sensitivity (Tallarini (2000)) or robustness (Barillas, Hansen, and Sargent (2009)). We estimate the parameters of the endowment process and find evidence of stochastic volatility in log consumption growth. Introducing stochastic volatility helps the model generate a more plausible unconditional market price of risk and increases the measured welfare costs of business cycles by about 15%. We propose novel algorithms to characterize and simulate the robust agent's worst case model. Using this methodology we find that the above asset pricing and welfare implications are due to an agent who fears that his consumption growth not only has a lower mean and higher variance than in his approximating model, but also displays disasters and persistence.

In a real business cycle model, an agent's fear of model misspecification interacts with stochastic volatility to induce time varying worst case scenarios. These time varying worst case scenarios capture a notion of animal spirits where the probability distributions used to evaluate decision rules and price assets do not necessarily reflect the fundamental characteristics of the economy. Households entertain a pessimistic view of the world and their pessimism varies with the overall level of volatility in the economy, implying an amplification of the effects of volatility shocks. By using perturbation methods and Monte Carlo techniques we extend the class of models analyzed with robust control methods to include the sort of nonlinear production-based DSGE models that are popular in academic research and policymaking practice.