We consider a nonparametric method to estimate conditional expected shortfalls, i.e. conditional expected losses knowing that losses are larger than a given loss quantile. We derive the asymptotic properties of kernal estimators of conditional expected shortfalls in the context of a stationary...

Much of the traditional economic theory of insurance is based on the assumption that the risk against which insurance is to be purchased is entirely exogenous. This is usually modelled by simply allowing the individual to include insurance as a mechanism of covering risk, without any real...

We study a test statistic on the integrated squared difference between a kernel estimator of the copula density and a kernel smoothed estimator of the parametric copula density. We show for fixed smoothing parameters that the test is consistent and that the asymptotic properties are driven by a...

We consider distributional free inference to test for positive quadrant dependence, i.e.for the probability that two variables are simultaneously small (or large) being at least as great as it would be were they dependent. Tests for its generalisation in higher dimensions, namely positive...

In this paper, we characterize explicitly the first derivative of the Value at Risk and the Expected Shortfall with respect to portfolio allocation when netting between positions exists. As a particular case, we examine a simple Gaussian example in order to illustrate the impact of netting...

We propose inference tools to analyse the ordering of concordance of random vectors. The analysis in the bivariate case relies on tests for upper and lower quadrant dominance of the true distribution by a parametric or semiparametric model, i.e. for a parametric or semiparametric model to give a...

We consider a nonparametric method to estimate copulas, i.e. functions linking joint distributions to their univariate margins. We derive the asymptotic properties of kernel estimators of copulas and their derivatives in the context of a multivariate stationary process satisfactory strong mixing...

We consider a consistent test, that is similar to a Kolmogorov-Smirnov test, of the complete set of restrictions that relate to the copula representation of positive quadrant dependence. For such a test we propose and justify inference relying on a simulation based multiplier method and a...