Adaptive Bernstein Copulas and Risk Management

TL;DR

This paper introduces a new method for constructing Bernstein copulas with an admissible discrete skeleton, improving dependence modeling and risk measure estimation efficiency in risk management applications.

Contribution

It proposes a constructive approach to Bernstein copulas with an admissible discrete skeleton, reducing overfitting and simulation effort in high-dimensional dependence modeling.

Findings

Reduced overfitting in dependence models

Improved efficiency in simulation for Bernstein copulas

Effective comparison of Bernstein and Gaussian copulas in risk estimation

Abstract

We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we compare different approaches of Bernstein and Gaussian copulas w.r.t. the estimation of risk measures in risk management.