Risk and Risk Aversion: A State-Space Approach, with Applications.

The objective of this project is to develop a new theory of choice under uncertainty based on agents' attitudes toward uncertainty when uncertainty is described by (a finite set of) states of nature. Implications of the new theory for consumption allocations and prices of financial assets in equilibrium are studied too. The main attitude toward uncertainty this project is concerned with is risk aversion. Risk aversion gives rise to many important results in financial economics. The most frequently used specification of risk-averse preferences is the concave expected utility. But this is very restrictive and has little empirical or experimental support. Further, it has no satisfactory axiomatic foundation in the relevant setting. The occasionally used more general class of risk-averse preferences - utility functions that are monotone with respect to second order stochastic dominance - has proved to be, with exception of some special cases, very difficult to characterize. This project studies a new alternative class of utility functions that is broader than monotone functions with respect to second order stochastic dominance but yet can be used to obtain very useful results on portfolio choice, risk sharing, asset pricing and other areas of financial economics.

The project explores a new notion of 'greater risk' based on the idea of risk as a mean-independent random variable (a state-contingent claim) with zero mean. The project introduces a class of utility functions that are monotone with respect to greater risk. Greater risk is far stronger than the standard Rothschild-Stiglitz (or second order stochastic dominance) notion of more risky. One difference is that two contingent claims with the same distribution are not considered equivalent under ordering by greater risk, in contrast to the Rothschild-Stiglitz notion. There is no appealing reason that they should be considered equivalent.

The class of utility functions that are monotone with respect to greater risk (called averse to mean-independent risk) has a nice characterization. Again, this is in contrast to functions that are monotone with respect to second order stochastic dominance for which there is no useful general characterization. The second important advantage of the class of mean-independent risk-averse utility functions is that, as all important results in the theory of financial markets - most of them known under the assumption of risk-averse expected utility - carry over to that much broader class of functions.