Using regular variation to define heavy tailed distributions, we show that prominent downside risk measures produce similar and consistent ranking of heavy tailed risk. Thus regardless of the particular risk measure being used, assets will be ranked in a similar and consistent manner for heavy...

In this paper we compare overall as well as downside risk measures with respect to the criteria of first and second order stochastic dominance. While the downside risk measures, with the exception of tail conditional expectation, are consistent with first order stochastic dominance, overall risk...

This paper explores the potential for violations of VaR subadditivity both theoretically and by simulations, and finds that for most practical applications VaR is subadditive. Hence, there is no reason to choose a more complicated risk measure than VaR, solely for reasons of coherence.

Economic problems such as large claims analysis in insurance and value-at-risk in finance, require assessment of the probability P of extreme realizations Q. This paper provides a semi-parametric method for estimation of extreme (P,Q) combinations for data with heavy tails. We solve the long...

We characterize the investor’s optimal portfolio allocation subject to a budget constraint and a probabilistic VaR constraint in complete markets environments with a finite number of states. The set of feasible portfolios might no longer be connected or convex, while the number of local optima...

Under the new Capital Accord, banks choose between two different types of risk management systems, the standard or the internal rating based approach. The paper considers how a bank's preference for a risk management system is affected by the presence of supervision by bank regulators. The model...

Accurate prediction of extreme events are of primary importance in many financial applications. The properties of historical simulation and Risk Metrics techniques for computing Valu-at Risk (VaR) are compared with a method which involves modelling the tails of financial returns explicitly with...

Complex interactions between fundamentals and liquidity during unstable periods in financial markets are succinctly modeled with coordination games. We propose a flexible framework to estimate such a model and use the efficient method of moments as estimation procedure. We illustrate the model...

Many financial applications, such as risk analysis and derivatives pricing, depend on time scaling of risk.  A common method for this purpose, though only correct when returns are iid normal, is the square root of time rule where an estimated quantile of a return distribution is scaled to a...