On the asymptotics of value-at-risk for portfolio loss under bivariate Eyraud-Farlie-Gumbel-Morgenstern copula and heavy tails

In the setting of bivariate Eyraud-Farlie-Gumbel-Morgenstern copula and heavy tails characterized by the power law of tail decay, we give the asymptotics of value-at-risk for portfolio loss as the confidence level tends to one. It can be seen from the obtained asymptotics that diversification decreases the value-at-risk of portfolio loss for the tail index greater than one and increases the value-at-risk of portfolio loss for the tail index less than one. To illustrate the obtained results, a relevant example is shown.