A Form of Multivariate Pareto Distribution With Applications to Financial Risk Measurement

Su, Jianxi; Furman, Edward

doi:10.1017/asb.2016.22

Cited by 44 publications

(33 citation statements)

References 36 publications

(70 reference statements)

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“…This has been extensively argued and illustrated by, e.g., Furman and Zitikis [13,15], Su [33], Su and Furman [34]; see also references therein. Therefore, elegant formulas and relationships for capital allocations are available in the cases such as the multivariate elliptical distribution, and in particular we have the equations C the rst moments…”

Section: Remarkmentioning

confidence: 80%

CMPH: a multivariate phase-type aggregate loss distribution

Ren

Zitikis

2017

Dependence Modeling

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Abstract:We introduce a compound multivariate distribution designed for modeling insurance losses arising from di erent risk sources in insurance companies. The distribution is based on a discrete-time Markov Chain and generalizes the multivariate compound negative binomial distribution, which is widely used for modeling insurance losses. We derive fundamental properties of the distribution and discuss computational aspects facilitating calculations of risk measures of the aggregate loss, as well as allocations of the aggregate loss to individual types of risk sources. Explicit formulas for the joint moment generating function and the joint moments of di erent loss types are derived, and recursive formulas for calculating the joint distributions given. Several special cases of particular interest are analyzed. An illustrative numerical example is provided.

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Section: Remarkmentioning

confidence: 80%

CMPH: a multivariate phase-type aggregate loss distribution

Ren

Zitikis

2017

Dependence Modeling

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“…The bivariate elliptical distribution also has a linear regression function (e.g., Zitikis, 2008, 2017), and so do several bivariate Pareto distributions, though of course not all of them. For details and examples, we refer to Su (2016), Su and Furman (2017), and references therein.…”

Section: Resultsmentioning

confidence: 99%

Statistical foundations for assessing the difference between the classical and weighted-Gini betas

Gribkova

Zitikis

2017

Math. Meth. Stat.

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Abstract. The 'beta' is one of the key quantities in the capital asset pricing model (CAPM).In statistical language, the beta can be viewed as the slope of the regression line fitted to financial returns on the market against the returns on the asset under consideration. The insurance counterpart of CAPM, called the weighted insurance pricing model (WIPM), gives rise to the so-called weighted-Gini beta. The aforementioned two betas may or may not coincide, depending on the form of the underlying regression function, and this has profound implications when designing portfolios and allocating risk capital. To facilitate these tasks, in this paper we develop large-sample statistical inference results that, in a straightforward fashion, imply confidence intervals for, and hypothesis tests about, the equality of the two betas.

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“…Except for well-known risk measures, including value at risk [6] or coherent and convex risk measures [7], there are many others methods that authors use to measure financial risks. Su and Furman [8] apply a form of multivariate Pareto distribution to measure financial risks. Spatial financial time series models were introduced by Blasques et al [9], Yang et al [10] and Audrino and Barone-Adesi [11].…”

Section: Literature Reviewmentioning

confidence: 99%

Financial Risk Measurement and Prediction Modelling for Sustainable Development of Business Entities Using Regression Analysis

et al. 2018

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Abstract:The issue of the debt, bankruptcy or non-bankruptcy of a company is presented in this article as one of the ways of conceiving risk management. We use the Amadeus database to obtain the financial and accounting data of Slovak enterprises from 2015 and 2016 to calculate the most important financial ratios that may affect the financial health of the company. The main aim of the article is to reveal financial risks of Slovak entities and to form a prediction model, which is done by the identification of significant predictors having an impact on the health of Slovak companies and their future prosperity. Realizing the multiple regression analysis, we identified the significant predictors in conditions of the specific economic environment to estimate the corporate prosperity and profitability. The results gained in the research are extra important for companies themselves, but also for their business partners, suppliers and creditors to eliminate financial and other corporate risks related to the unhealthy or unfavorable financial situation of the company.

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A Form of Multivariate Pareto Distribution With Applications to Financial Risk Measurement

Cited by 44 publications

References 36 publications

CMPH: a multivariate phase-type aggregate loss distribution

CMPH: a multivariate phase-type aggregate loss distribution

Statistical foundations for assessing the difference between the classical and weighted-Gini betas

Financial Risk Measurement and Prediction Modelling for Sustainable Development of Business Entities Using Regression Analysis

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