Adaptive Bernstein Copulas and Risk Management

Pfeifer, Dietmar; Ragulina, Olena

doi:10.3390/math8122221

Cited by 5 publications

(1 citation statement)

References 22 publications

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“…This is why beta r.v. is widely used in Bayesian statistics [22], simulation [23,24], management and production models [25][26][27], control systems [28], and in the study of genome structures [29], machine learning [30], among many others.…”

Section: Preliminariesmentioning

confidence: 99%

Critical Analysis of Beta Random Variable Generation Methods

Almaraz Luengo,

Gragera

2023

Mathematics

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The fast generation of values of the beta random variable is a subject of great interest and multiple applications, ranging from purely mathematical and statistical ones to applications in management and production, among others. There are several methods for generating these values, with one of the essential points for their design being the selection of random seeds. Two interesting aspects converge here: the use of sequences as inputs (and the need for them to verify properties such as randomness and uniformity, which are verified through statistical test suites) and the design of the algorithm for the generation of the variable. In this paper, we analyse, in detail, the algorithms that have been developed in the literature, both from a mathematical/statistical and computational point of view. We also provide empirical development using R software, which is currently in high demand and is one of the main novelties with respect to previous comparisons carried out in FORTRAN. We establish which algorithms are more efficient and in which contexts, depending on the different values of the parameters, allowing the user to determine the best method given the experimental conditions.

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Section: Preliminariesmentioning

confidence: 99%

Critical Analysis of Beta Random Variable Generation Methods

Almaraz Luengo,

Gragera

2023

Mathematics

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Generating unfavourable VaR scenarios under Solvency II with patchwork copulas

Pfeifer

Ragulina

2021

Dependence Modeling

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The central idea of the paper is to present a general simple patchwork construction principle for multivariate copulas that create unfavourable VaR (i.e. Value at Risk) scenarios while maintaining given marginal distributions. This is of particular interest for the construction of Internal Models in the insurance industry under Solvency II in the European Union. Besides this, the Delegated Regulation by the European Commission requires all insurance companies under supervision to consider different risk scenarios in their risk management system for the company’s own risk assessment. Since it is unreasonable to assume that the potential worst case scenario will materialize in the company, we think that a modelling of various unfavourable scenarios as described in this paper is likewise appropriate. Our explicit copula approach can be considered as a special case of ordinal sums, which in two dimensions even leads to the technically worst VaR scenario.

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A multi-parameter Generalized Farlie-Gumbel-Morgenstern bivariate copula family via Bernstein polynomial

Susam

2022

Hacettepe Journal of Mathematics and Statistics

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In this paper, we are proposing a flexible method for constructing a bivariate generalized Farlie-Gumbel-Morgenstern (G-FGM) copula family. The method is mainly developed around the function ϕ(t) (t ∈ [0, 1]), where ϕ is the generator of the G-FGM copula. The proposed construction method has useful advantages. The first of which is the direct relationship between the ϕ function and Kendall's tau. The second advantage is the possibility of constructing a multi-parameter G-FGM copula which allows us to better harmonize empirical instruction with the model. The construction method is illustrated by three real data examples.

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Adaptive Bernstein Copulas and Risk Management

Cited by 5 publications

References 22 publications

Critical Analysis of Beta Random Variable Generation Methods

Critical Analysis of Beta Random Variable Generation Methods

Generating unfavourable VaR scenarios under Solvency II with patchwork copulas

A multi-parameter Generalized Farlie-Gumbel-Morgenstern bivariate copula family via Bernstein polynomial

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