Accurate prediction of the frequency of extreme events is of primary importance in many financialapplications such as Value-at-Risk (VaR) analysis. We propose a semi-parametric method for VaRevaluation. The largest risks are modelled parametrically, while smaller risks are captured by the...

Large data sets in finance with millions of observations have becomewidely available. Such data sets enable the construction of reliablesemi-parametric estimates of the risk associated with extreme pricemovements. Our approach is based on semi-parametric statisticalextreme value analysis, and...

Risk managers use portfolios to diversify away the unpriced risk of individual securities. In this article we compare the benefits of portfolio diversification for downside risk in case returns are normally distributed with the case of fat-tailed distributed returns. The downside risk of a...

We advocate the use of absolute moment ratio statistics in conjunctionwith standard variance ratio statistics in order to disentangle lineardependence, non-linear dependence, and leptokurtosis in financial timeseries. Both statistics are computed for multiple return horizonssimultaneously, and...

The paper characterizes first and second order tail behavior ofconvolutions of i.i.d. heavy tailed random variables with supporton the real line. The result is applied to the problem of riskdiversification in portfolio analysis and to the estimation of theparameter in a MA(1) model.

The stock market collapse led to political tensions between generations due to the fuzzy definition of the property rights over the pension funds’ wealth. The problem is best resolved by the introduction of generational accounts. Modern consumption and portfolio theory shows that the younger...

Portfolio risk is in an important way driven by 'abnormal' returns emanating from heavy tailed distributed asset returns. The theory of regular variation and extreme values provides a model for this feature of financial data. We first review this theory and subsequently study the problem of...

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...