In a Markov decision problem with hidden state variables, a posterior distribution serves as a state variable and Bayes ’ law under an approximating model gives its law of motion. A decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby when measured by their expected log likelihood ratios (entropies). Martingales represent alternative models. A decision maker constructs a sequence of robust decision rules by pretending that a sequence of minimizing players choose increments to a martingale and distortions to the prior over the hidden state. A risk sensitivity operator induces robustness to perturbations of the approximating model conditioned on the hidden state. Another risk sensitivity operator induces robustness to the prior distribution over the hidden state. We use these operators to extend the approach of Hansen and Sargent (1995) to problems that contain hidden states. 1

We study an investor’s optimal consumption and portfolio choice problem when he confronts with two possibly misspecified submodels of stock returns: one with IID returns and the other with predictability. We adopt a generalized recursive ambiguity model to accommodate the investor’s aversion to model uncertainty. The investor deals with specification doubts by slanting his beliefs about submodels of returns pessimistically, causing his investment strategy to be more conservative than the Bayesian strategy. This effect is large for high and low values of the predictive variable. Unlike in the Bayesian framework, the hedging demand against model uncertainty may cause the investor’s stock allocations to first decrease sharply and then increase with his prior probability of the IID model, even when the expected stock return under the IID model is lower than under the predictability model. Adopting suboptimal investment strategies by ignoring model uncertainty can lead to sizable welfare costs.

High-interest-rate currencies tend to appreciate in the future relative to low-interest-rate currencies instead of depreciating as uncovered-interest-parity (UIP) predicts. I construct a model of exchange-rate determination in which ambiguity-averse agents face a dynamic filtering problem featuring signals of uncertain precision. Solving a max-min problem, agents act upon a worstcase signal precision and systematically underestimate the hidden state that controls payoffs. Thus, on average, agents next periods perceive positive innovations, which generates an upward reevaluation of the strategy’s profitability and implies ex-post departures from UIP. The model also produces predictable expectational errors, negative skewness and time-series momentum for currency speculation payoffs.

We develop a consumption-based asset-pricing model in which the representative agent is ambiguous about the hidden state in consumption growth. He learns about the hidden state under ambiguity by observing past consumption data. His preferences are represented by the smooth ambiguity model axiomatized by Klibanoff et al. (2005, 2006). Unlike the standard Bayesian theory, this utility model implies that the posterior of the hidden state and the conditional distribution of the consumption process given a state cannot be reduced to a predictive distribution. By calibrating the ambiguity aversion parameter, the subjective discount factor, and the risk aversion parameter (with the latter two values between zero and one), our model can match the first moments of the equity premium and riskfree rate found in the data. In addition, our model can generate a variety of dynamic asset pricing phenomena, including the procyclical variation of price-dividend ratios, the countercyclical variation of equity premia and equity volatility, and the mean reversion and long horizon predictability of excess returns.

Recent work shows that concerns about (i) long run expected growth and (ii) uncertainty about future economic prospects, drive asset prices. These two channels of economic risks can account for the risk premia and asset price fluctuations. Hence, the long run risks model potentially provides a coherent and systematic framework for

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Epstein (2009) describes three Ellsberg-style thought experiments and argues that they pose di ¢ culties for the smooth ambiguity model of decision making under uncertainty developed by Klibano¤, Marinacci and Mukerji (2005). We revisit these thought experiments and …nd, to the contrary, that they either point to strengths of the smooth ambiguity model compared to other models, such as the maxmin expected utility model (Gilboa and Schmeidler, 1989), or, in the case of one thought experiment, raise criticisms that apply equally to a broad range of current ambiguity models. 1

This paper studies the quantitative implications of the interaction between robust control and stochastic volatility for key asset pricing phenomena. We present an equilibrium term structure model in which output growth is conditionally heteroskedastic. The agent does not know the true model of the economy and chooses optimal policies that are robust to model misspeci…cation. The choice of robust policies greatly ampli…es the e¤ect of conditional heteroskedasticity in consumption growth, improving the model’s ability to explain asset prices. In a robust control framework, stochastic volatility in consumption growth generates both a state-dependent market price of model uncertainty and a stochastic market price of risk. We estimate the model using data from the bond and equity markets, as well as consumption data. We show that the model is consistent with key empirical regularities that characterize the bond and equity markets. We also characterize empirically the set of models the robust representative agent entertains, and show that this set is ‘small’. In other words, it is statistically di ¢ cult to distinguish between models in this set.

This paper studies the quantitative implications of the interaction between robust control and stochastic volatility for key asset pricing phenomena. We present an equilibrium term structure model in which output growth is conditionally heteroskedastic. The agent does not know the true model of the economy and chooses optimal policies that are robust to model misspeci…cation. The choice of robust policies greatly ampli…es the e¤ect of conditional heteroskedasticity in consumption growth, improving the model’s ability to explain asset prices. In a robust control framework, stochastic volatility in consumption growth generates both a state-dependent market price of model uncertainty and a stochastic market price of risk. We estimate the model using data from the bond and equity markets, as well as consumption data. We show that the model is consistent with key empirical regularities that characterize the bond and equity markets. We also characterize empirically the set of models the robust representative agent entertains, and show that this set is ‘small’. In other words, it is statistically di ¢ cult to distinguish between models in this set.

Using factor based approaches, we investigate a return and volatility forecasting procedure that exploits all the available information by still keeping the econometric framework at considerable size. Our findings demonstrate that factor based approaches provide substantial gains when predicting the sign of the excess returns and state of the volatility separately as well as jointly. A striking result is that the performance of this procedure increases especially after 1990, where the existing evidence suggests lower predictive power of many econometric forecasting procedures. For evaluating the economic significance of the factor based approach, we also simulate a mean-variance investor that uses return and volatility forecasts to determine optimal portfolio weights. In line with the predictive performance, under moderate transaction costs, a mean-variance investor would be willing to pay several hundreds of basis points per annum for switching from passive and dynamic strategies based on benchmark models to dynamic strategies that employ factor based approaches after 1990.