Risk aggregation and capital allocation using a new generalized Archimedean copula

TL;DR

This paper introduces a new mixed Bernstein copula to model dependence in risk aggregation, providing explicit formulas for risk measures and capital allocation, enhancing flexibility over traditional Archimedean copulas.

Contribution

It proposes a novel generalized copula for better modeling of risk dependence, with explicit formulas for risk measures and allocations.

Findings

Derived closed-form expressions for tail value-at-risk (TVaR)

Provided explicit formulas for aggregate risk distribution

Enhanced modeling flexibility over traditional copulas

Abstract

In this paper, we address risk aggregation and capital allocation problems in the presence of dependence between risks. The dependence structure is defined by a mixed Bernstein copula which represents a generalization of the well-known Archimedean copulas. Using this new copula, the probability density function and the cumulative distribution function of the aggregate risk are obtained. Then, closed-form expressions for basic risk measures, such as tail value-at-risk(TVaR) and TVaR-based allocations, are derived.