多维随机变量样本均值差的随机比较

多元椭圆分布的随机序

Stochastic Orderings of Multivariate Elliptical Distributions

本文建立椭圆随机向量期望差恒等式，统一推导多元椭圆分布按积分随机序分类的充要条件，获得新不等式并推广正态情形结果。

Ordering of multivariate probability distributions with respect to extreme portfolio losses

A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of ordering conditions on the spectral measures, which allows for analytical or numerical verification in practical applications. Additional comparison criteria in terms of further stochastic orderings are derived. The application examples include worst case and best case scenarios, elliptically contoured distributions, and multivariate regularly varying models with …

A comparison of techniques for dynamic multivariate risk measures

This paper contains an overview of results for dynamic multivariate risk measures. We provide the main results of four different approaches. We will prove under which assumptions results within these approaches coincide, and how properties like primal and dual representation and time consistency in the different approaches compare to each other.

Comparison results for Garch processes

We consider the problem of stochastic comparison of general Garch-like processes, for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the Garch process itself, and discuss their interpretations. We focus on the convex order and show that in the case of symmetric innovations it is also propagated to the cumulated sums of the Garch process. More generally, we discuss multivariate comparison results related to the multivariate convex and supermodular order. Finally we discuss ordering with respe…

Multivariate Optimized Certainty Equivalent Risk Measures and their Numerical Computation

We present a framework for constructing multivariate risk measures that is inspired from univariate Optimized Certainty Equivalent (OCE) risk measures. We show that this new class of risk measures verifies the desirable properties such as convexity, monotonocity and cash invariance. We also address numerical aspects of their computations using stochastic algorithms instead of using Monte Carlo or Fourier methods that do not provide any error of the estimation.

On Multivariate Extensions of Value-at-Risk

In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level sets of multivariate distribution functions whereas the upper-orthant VaR is constructed from level sets of multivariate survival functions. Several properties have been derived. In particular, we show that these risk measures both satisfy the positive homogeneity and the translation invariance propert…