Bayesian nonparametric copulas with tail dependence
The paper develops Bayesian nonparametric copulas via generalized partitions and stick-breaking, modeling asymmetry and tail dependence for risk management.
What it examines
This paper introduces Bayesian nonparametric copulas using generalized partitions of unity with a Dirichlet process prior. The approach designs RGPU copulas that capture asymmetry and tail dependence, employing stick-breaking and MCMC methods to improve risk modeling in finance and insurance.
What it concludes
The study shows NB-Dirichlet copulas provide better tail and asymmetry modeling than existing methods. This approach applies to risk assessment in insurance and financial portfolios. Future research will extend the method to multivariate settings with adaptive smoothing for improved risk management.
Evidence objects
Researchers introduce a groundbreaking approach using Random GPU copulas with a Negative Binomial Dirichlet model, capturing tail dependence and asymmetry while outperforming traditional parametric copulas through a Bayesian nonparametric framework.
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Introducing a novel GPU-Dirichlet prior, the paper integrates Bernstein polynomials with Dirichlet process mixtures, applying extensive simulations and real-world insurance and bank datasets to demonstrate superior predictive performance effectively overall.
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Utilizing a robust MCMC slice sampler, the study emphasizes scalability despite noting a uniform smoothing parameter may restrict practical flexibility, prompting calls for further development across multiple dimensions in practice.
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Introducing a novel Bayesian nonparametric copula model, this paper innovatively captures central and tail dependencies in joint distributions via $\text{infinite mixtures}$ and stick-breaking representation. It overcomes limitations of standard parametric copulas, offering a unique perspective. This fresh approach is compelling for quantitative risk management, delivering significant contributions and remarkably valuable insights.
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Raw abstract and provenance
Abstract: We introduce a novel bivariate copula model able to capture both the central and tail dependence of the joint probability distribution. Model that can capture the dependence structure within the joint tail have important implications in many application areas where the focus is risk management (e.g. macroeconomics and finance). We use a Bayesian nonparametric approach to introduce a random copula… ▽ More We introduce a novel bivariate copula model able to capture both the central and tail dependence of the joint probability distribution. Model that can capture the dependence structure within the joint tail have important implications in many application areas where the focus is risk management (e.g. macroeconomics and finance). We use a Bayesian nonparametric approach to introduce a random copula based on infinite partitions of unity. We define a hierarchical prior over an infinite partition of the unit hypercube which has a stick breaking representation leading to an infinite mixture of products of independent beta densities. Capitalising on the stick breaking representation we introduce a Gibbs sample to proceed to inference. For our empirical analysis we consider both simulated and real data (insurance claims and portfolio returns). We compare both our model's ability to capture tail dependence and its out of sample predictive performance to competitive models (e.g. Joe and Clayton copulas) and show that in both simulated and real examples our model outperforms the competitive models. △ Less
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