scholarly journals Hoeffding–Sobol decomposition of homogeneous co-survival functions: from Choquet representation to extreme value theory application

2021 ◽  
Vol 9 (1) ◽  
pp. 179-198
Author(s):  
Cécile Mercadier ◽  
Paul Ressel
Keyword(s):  
Random Vector ◽  
Extreme Value Theory ◽  
Tail Dependence ◽  
Value Theory ◽  
Extreme Value ◽  
Survival Functions ◽  
Main Ingredient ◽  
Asymptotic Dependence ◽  
Dependence Function ◽  
Theory Application

Abstract The paper investigates the Hoeffding–Sobol decomposition of homogeneous co-survival functions. For this class, the Choquet representation is transferred to the terms of the functional decomposition, and in addition to their individual variances, or to the superset combinations of those. The domain of integration in the resulting formulae is reduced in comparison with the already known expressions. When the function under study is the stable tail dependence function of a random vector, ranking these superset indices corresponds to clustering the components of the random vector with respect to their asymptotic dependence. Their Choquet representation is the main ingredient in deriving a sharp upper bound for the quantities involved in the tail dependograph, a graph in extreme value theory that summarizes asymptotic dependence.

Tail dependence analysis of stock markets using extreme value theory

2017 ◽  
Vol 49 (45) ◽  
pp. 4588-4599
Author(s):  
Abhay K. Singh ◽  
David E. Allen ◽  
Robert J. Powell
Keyword(s):  
Extreme Value Theory ◽  
Stock Markets ◽  
Tail Dependence ◽  
Value Theory ◽  
Extreme Value ◽  
Dependence Analysis

AN EXTREME VALUE THEORY APPROACH TO THE ALLOCATION OF MULTIPLE ASSETS

2004 ◽  
Vol 07 (08) ◽  
pp. 1031-1068 ◽  
Author(s):  
BRENDAN O. BRADLEY ◽  
MURAD S. TAQQU
Keyword(s):  
Extreme Value Theory ◽  
Asset Allocation ◽  
Equity Markets ◽  
Value Theory ◽  
Extreme Value ◽  
Theory Approach ◽  
Asymptotic Dependence ◽  
International Equity Markets ◽  
Variable Approach ◽  
International Equity

We investigate the portfolio construction problem for risk-averse investors seeking to minimize quantile based measures of risk. Using dependence measures from extreme value theory, we find that most international equity markets are asymptotically independent. We also find that the few cases of asymptotic dependence occur mostly in markets which are in close geographic proximity. We then examine how extremal dependence affects the asset allocation problem. Following the structure variable approach, we focus on the portfolio and model its tail in a manner consistent with extreme value theory. We then develop a methodology for asset allocation where the goal is to guard against catastrophic losses. The methodology is tested through simulations and applied to portfolios made up of two or more international equity markets. We analyze in detail three typical types of markets, one where the assets are asymptotically independent and the ratio of marginal risks is not constant, the second where the assets are asymptotically independent but the ratio of marginal risks are approximately constant and the third where the assets are asymptotically dependent and the ratio of marginal risks is not constant. The results are compared with the optimal portfolio under the assumption of normally distributed returns. Surprisingly, we find that the assumption of normality incurs only a modest amount of extra risk for all but the largest losses. We make the software written in support of this work freely available and describe its use in the appendix.

scholarly journals The modeling of extreme stochastic dependence using copulas and extreme value theory: case study from energy prices

2017 ◽  
Vol 5 (2) ◽  
pp. 29
Author(s):  
ömer önalan
Keyword(s):  
Extreme Value Theory ◽  
Probability Distributions ◽  
Random Variables ◽  
Tail Dependence ◽  
Value Theory ◽  
Extreme Value ◽  
Energy Prices ◽  
Multivariate Distributions ◽  
Data Set ◽  
Stochastic Dependence

In this paper, we investigate the properties of tail dependence with an approach which is based on the copula models and extreme value theory to obtain a joint distribution function of extreme events and to quantify the dependence between random variables. To achieve this objective, we quantify the large co-movements between the random variables returns which are based on the data set daily quotes of exceeds the threshold value of random variables. In this study, stochastic dependence was modeled by the copulas which it provides a good approach for constructing multivariate probability distributions with flexible marginal’s and different forms of dependence. Choosing the right copula is very important in modeling. The multivariate distributions are easily simulated using the copulas. Finally we can describe the copula family which correctly represents the dependence. To demonstrate the usefulness of the proposed models, we confine our analysis to big price changes of energy commodity spot prices. The empirical findings demonstrated that the copula model which is combined the extreme value theory is a good approach to model the together extreme large changes.

709 Evaluation of food risk exposure using extreme value theory-application to heavy metals for sea products consumers

2003 ◽  
Vol 144 ◽  
pp. s190 ◽  
Author(s):  
J. Tressou ◽  
P. Bertail ◽  
A. Crepet ◽  
M. Feinberg ◽  
J.-Ch. Leblanc
Keyword(s):  
Heavy Metals ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Risk Exposure ◽  
Theory Application
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