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...

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 provided a semi-parametric method for estimation of extreme (P, Q) combinations for data with heavy tails. We solve the long...

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

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...

We use a subsample bootstrap method to get a consistent estimate of the asymptotically optimal choice of the sample fraction, in the sense of minimal mean squared error, which is needed for tail index estimation. Unlike previous methods our procedure is fully self contained. In particular, the...

Large data sets in finance with millions of observations have become widely available. Such data sets enable the construction of reliable semi-parametric estimates of the risk associated with extreme price movements. Our approach is based on semi-parametric statistical extreme value analysis,...