On uniform tail expansions of bivariate copulas

• Autorzy: Piotr Jaworski
• Języki publikacji: EN

Abstrakty

EN

The theory of copulas provides a useful tool for modelling dependence in risk management. The goal of this paper is to describe the tail behaviour of bivariate copulas and its role in modelling extreme events. We say that a bivariate copula has a uniform lower tail expansion if near the origin it can be approximated by a homogeneous function L(u,v) of degree 1; and it is said to have a uniform upper tail expansion if the associated survival copula has a lower tail expansion. In this paper we (1) introduce the notion of the uniform tail expansion of a bivariate copula; (2) describe the main properties of the leading part L(u,v) like two-monotonicity or concavity; (3) determine the set of all possible leading parts L(u,v); (4) compute the leading parts of the uniform tail expansions for the most popular copulas like gaussian, archimedean or BEV; (5) apply uniform tail expansions in estimating the extreme risk of a portfolio consisting of long positions in risky assets.

Kategorie tematyczne

• 62H20: Measures of association (correlation, canonical correlation, etc.)
• 62E20: Asymptotic distribution theory
• 91B30: Risk theory, insurance

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2004
• Tom: 31
• Numer: 4
• Strony: 397-415

Daty

wydano

2004

Twórcy

autor

Piotr Jaworski

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/am31-4-2