Probability statements about future evolutions of financial and actuarial risks are expressed in terms of the ‘real-world' probability measure P, whereas in an arbitrage-free environment, the prices of these traded risks can be expressed in terms of an equivalent martingale measure Q. The...

In order to price multivariate derivatives, there is need for a multivariate stock price model. To keep the simplicity and attractiveness of the one-dimensional Black & Scholes model, one often considers a multivariate model where each individual stock follows a Black & Scholes model, but the...

Distorted expectations can be expressed as weighted averages of quantiles. In this note, we show that this statement is true, but that one has to be careful with the correct formulation of it. Furthermore, the proofs of the additivity property for distorted expectations of a comonotonic sum that...

Nonextreme regression quantiles are estimated nonparametrically on the basis of local polynomial approximations to the true conditional quantile function. The consistency of the estimator is shown. The asymptotic normality is proven and the asymptotic confidence interval for the regression...

In this paper we show that under appropriate moment conditions, two supermodular ordered random vectors with equal expected utilities (or distorted expectations) of the sums for an appropriate utility (or distortion) function, must necessarily be equal in distribution. The results in this paper...

In this paper we show that under appropriate moment conditions, the supermodular ordered random vectors X = (X1, X2, ... , Xn) and Y = (Y1, Y2, ... ,Yn) with equal expected utilities (or distorted expectations) of the sums X1 + X2 + ... + Xn and Y1 + Y2 + ... + Yn for an appropriate utility (or...

For any random vector X = (X1; ...;Xn) on a given probability space (Ω;F;Pr), one can always instruct comonotonic modi cations of X, which are de ned as random vectors with the same marginals as X but with the comonotonic copula describing their dependency structure. In this short note, we...

The paper explores the effect of measurement errors on the estimation of a linear panel data model. The conventional fixed effects estimator, which ignores measurement errors, is biased. By correcting for the bias one can construct consistent and asymptotically normal estimators. In addition, we...

The paper studies the problem of estimating the upper end point of a finite interval when the data come from a uniform distribution on this interval and are disturbed by normally distributed measurement errors with known variance. Maximum likelihood and method of moments estimators are...