In this paper we establish a one-to-one correspondence between lawinvariant convex risk measures on L∞ and L. This proves that the canonical model space for the predominant class of law-invariant convex risk measures is L.

This paper studies the cross-sectional risk-return trade-off in the stock market. A fundamental principle in finance is the positive relation between risk and expected return, whereas recent empirical evidence suggests the opposite. We apply referencedependent preferences to shed light on this violation. Reference-dependent preferences (e.g., prospect theory) typically posit that when facing pr...

In this paper we study asymptotic consistency of law invariant convex risk measures and the corresponding risk averse stochastic programming problems for independent identically distributed data. Under mild regularity conditions we prove a Law of Large Numbers and epiconvergence of the corresponding statistical estimators. This can be applied in a straightforward way to establishing convergence...

This article discusses the determination of risk capital based on “aversion” functions. Aversion functions weigh different outcomes according to perceived severity. Many practical and popular risk measures are usefully viewed in terms of aversion functions including those arising from distortion operators and risk margin loadings. The approach of this paper builds on, unifies,and extends existi...

A recent paper by Prékopa (2012) presented results in connection with Multivariate Value-at-Risk (MVaR) that has been known for some time under the name of p-quantile or p-Level Efficient Point (pLEP) and introduced a new multivariate risk measure, called Multivariate Conditional Value-at-Risk (MCVaR). The purpose of this paper is to further develop the theory and methodology of MVaR and MCVaR....

Quantitative risk management allows for qualitative notions such as optimality and expected returns to be put on a quantitative footing. It complements subjective risk considerations with an objective, statistical perspective. Broadly, quantitative risk management consists of two distinct elements. The first is measurement, which involves quantifying the overall risk of a portfolio. The second ...

Manski [2004] analyzes the relationship between the distribution of traders’ beliefs and the equilibrium price in a prediction market with risk neutral traders. He finds that there can be a substantial difference between the mean belief that an event will occur, and the price of an asset that pays one dollar if the event occurs and otherwise pays nothing. This result is puzzling, since these ma...

A monopolist typically defers entry into an industry as both price uncertainty and the level of relative risk aversion increase. The former attribute may be present in most deregulated industries, while the latter may be relevant for reasons of market incompleteness or the presence of technical uncertainty. By contrast, it has been shown that the presence of a rival hastens entry under risk neu...

Manski [2004] analyzes the relationship between the distribution of traders’ beliefs and the equilibrium price in a prediction market with risk neutral traders. He finds that there can be a substantial difference between the mean belief that an event will occur, and the price of an asset that pays one dollar if the event occurs and otherwise pays nothing. This result is puzzling, since these ma...

Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and give examples of such risk measures. We then discuss the statistical robustness of estimators of...