Monetary measures of risk like Value at Risk or Worst Conditional Expectation assess the risk of ÿnancial positions. The existing risk measures are of a static, one period nature. In this paper, I deÿne dynamic monetary risk measures and I present an axiomatic approach that extends the class of coherent risk measures to the dynamic framework. The axiom of translation invariance has to be recast as predictable translation invariance to account for the release of new information. In addition to the coherency axioms, I introduce the axiom of dynamic consistency. Consistency requires that judgements based on the risk measure are not contradictory over time. I show that consistent dynamic coherent risk measures can be represented as the worst conditional expectation of discounted future losses where the expectations are being taken over a set of probability measures that satisÿes a consistency condition.
We study competitive market outcomes in economies where agents have other-regarding preferences. We identify a separability condition on monotone preferences that is necessary and sufficient for one's own demand to be independent of the allocations and characteristics of other agents in the economy. Given separability, it is impossible to identify other-regarding preferences from market behavior: agents behave as if they had classical preferences that depend only on own consumption in competitive equilibrium. If preferences, in addition, depend only on the final allocation of consumption in society, the Second Welfare Theorem holds as long as an increase in resources can be distributed such that all agents are better off. Nevertheless, the First Welfare Theorem generally does not hold. Allowing agents to care about their own consumption and the distribution of consumption possibilities in the economy, we provide a condition under which agents have no incentive to make direct transfers, and show that this condition implies that competitive equilibria are efficient given prices.
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