On the asymptotics of tail conditional expectation for portfolio loss under bivariate Eyraud-Farlie-Gumbel-Morgenstern copula and heavy tails

Abstract

In the setting of bivariate Eyraud-Farlie-Gumbel-Morgenstern copula and heavy tails characterized by the power law of tail decay, we present the asymptotics of tail conditional expectation for portfolio loss as the confidence level tends to one. In order to illustrate the obtained result, a numerical example and its relevant simulation are carried out.

Keywords:

• Asymptotics
• Bivariate Eyraud-Farlie-Gumbel-Morgenstern copula
• Portfolio loss
• Power-law
• Tail conditional expectation

MATHEMATICS SUBJECT CLASSIFICATION (2000):

• 60F05
• 91B30

Acknowledgments

The authors are greatly grateful to the anonymous referees for providing valuable suggestions which improved the first manuscript. This paper is supported by the Natural Science Foundation of Shangrao Normal University (201804) and the National Science Foundation of China (11461009).