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This paper extends the analysis of HST to economies with equilibrium allocations that solve continuous time optimal resource allocation problems. Most of our results exploit the analytical convenience of continuous-time diusions. Working in continuous time lets us leave the con nes of a linear-quadratic framework: objective functions can be nonquadratic and state evolution equations can be nonlinear. Leaving the linearquadratic framework makes it easier to link our robustness parameter to commonly used measures of risk aversion both in decision problems and in security market data. It also gives us a general characterization of a precautionary mechanism in decision-making induced by a concern for robustness

We measure the extent to which the cyclical behavior of the turnover of equity shares on the NYSE can be accounted for by a single source of trade embedded in a one-sector neoclassical growth economy with dynamically complete markets. The source of trade is heterogeneity in agents ’ …nancial wealth. In the post-war U.S., turnover has been more than seven times as volatile as output, and has exhibited asynchronous cyclical characteristics: lagged turnover has co-varied positively with output; led turnover has co-varied negatively. The model, calibrated to match the mean behavior of asset returns and the distribution of wealth across U.S. households, accounts for up to 33 % of the volatility of turnover observed in the data. The asynchronous relationship observed between turnover and output is puzzling.

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This paper develops a measure of international systemic risk using a semi-structural approach. In particular, we work with a multi-country dynamic equilibrium setting, placing a constraint on the portfolio volatility of one of the countries. The tightening of this constraint is a channel through which shocks are propagated internationally in our model. The propagation of this financial constraint is what we define as systemic risk. In this paper we offer two estimation alternatives. First, we present a semi-structural approach in which we measure the tightness of the constraint using cross-equation restrictions from the model. The second approach is to implement a full structural estimation. We compare these two estimates with simple measures of systemic risk from principal components. We apply the two methodologies to the measurement of the systemic risk during the subprime crisis.

This paper studies an efficiency of a competitive equilibrium in an environment with a moral hazard problem and retrading possibility. The interaction between the private information problem and the possibility to retrade in ex post spot markets creates an externality unless preferences have a property such that the marginal rates of substitution between goods is independent of actions. The externality is internalized by allowing agents to contract ex ante on market fundamentals determining the spot prices, over and above contracting on actions and outputs, then competitive equilibria are equivalent with Pareto optima. Examples show that it is possible to have multiple market fundamentals in equilibrium. This market based solution concept is also applicable to an environment with preferences shock and retrading. Key words:

This paper analyzes the dynamic properties of portfolios that sustain dynamically complete markets equilibria when agents have heterogeneous priors. We argue that the conventional wisdom that belief heterogeneity generates continuous trade and signi…cant ‡uctuations in individual portfolios may be correct but it also needs some quali…cations. We consider an in…nite horizon stochastic endowment economy where the actual process of the states of nature consists in i.i.d. draws. The economy is populated by many Bayesian agents with heterogeneous priors over the stochastic process of the states of nature. Our approach hinges on studying portfolios that support Pareto optimal allocations. Since these allocations are typically history dependent, we propose a methodology to provide a complete recursive characterization when agents know that the process of states of nature is i.i.d. but disagree about the probability of the states. We show that even though heterogeneous priors within that class can indeed generate genuine changes in the portfolios of any dynamically complete markets equilibrium, these changes vanish with probability one if the support of every agent’s prior belief contains the true distribution. Finally, we provide examples in which asset trading does not vanish because either (i) no agent learns the true conditional probability of the states or (ii) some agent does not know the true process generating the data is i.i.d.

A competitive general equilibrium model with complete collateralized contracts under limited commitment is proposed and analyzed. With limited aggregate collateral, risk sharing is imperfect. There exists a minimal spanning set of finite collateralized contracts that generates the feasible space and that contains more than the complete set of collateralized Arrow securities. Examples show that exogenously restricting feasible contracts has a significant impact on agents ’ welfare. I prove that constrained optimal allocations can be decentralized as a general equilibrium with collateral constraints, and vice versa. Because a capital good serves as collateral, it has an additional value, called collateral premium. The collateral premium is zero if and only if risk sharing is perfect. This is a testable implication of the model.