Stochastic distortion and its transformed copula

Lin, Fan‐Chi; Peng, Liang; Xie, Jin; Yang, Jingping

doi:10.1016/j.insmatheco.2018.01.003

Cited by 9 publications

(4 citation statements)

References 47 publications

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“…In this case, a similar representation holds for the respective survival (or reliability) functions F (t) = q( Ḡ(t)), where q(u) = 1 − q(1 − u) is another distortion function, called dual distortion function. For further results on distorted distributions, see [32,38] and the references therein.…”

Section: Some Previous Definitions and Basic Resultsmentioning

confidence: 99%

Copula Representations for the Sum of Dependent Risks: Models and Comparisons

Navarro¹,

Sarabia²

2020

Prob. Eng. Inf. Sci.

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The study of the distributions of sums of dependent risks is a key topic in actuarial sciences, risk management, reliability and in many branches of applied and theoretical probability. However, there are few results where the distribution of the sum of dependent random variables is available in a closed form. In this paper, we obtain several analytical expressions for the distribution of the aggregated risks under dependence in terms of copulas. We provide several representations based on the underlying copula and the marginal distribution functions under general hypotheses and in any dimension. Then, we study stochastic comparisons between sums of dependent risks. Finally, we illustrate our theoretical results by studying some specific models obtained from Clayton, Ali-Mikhail-Haq and Farlie-Gumbel-Morgenstern copulas. Extensions to more general copulas are also included. Bounds and the limiting behavior of the hazard rate function for the aggregated distribution of some copulas are studied as well.

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Section: Some Previous Definitions and Basic Resultsmentioning

confidence: 99%

Copula Representations for the Sum of Dependent Risks: Models and Comparisons

Navarro¹,

Sarabia²

2020

Prob. Eng. Inf. Sci.

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“…In a risk assessment paradigm, several useful risk evaluation measures have been suggested, such as the value at risk (VaR), the tail conditional expectation (TCE), the distorted risk measures (DRM), and distortion risk measures based on copula (DRMC, in short)for pertinent reference in this context, see [8] and the references cited therein. For a real number θ in (0, 1), the TCE of a risk Y will be:…”

Section: Copula-based Conditional Tail Expectation For Kumaraswamy Dispersion Modelsmentioning

confidence: 99%

Tail Conditional Expectations Based on Kumaraswamy Dispersion Models

Ghosh¹,

Marques²

2021

Mathematics

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Recently, there seems to be an increasing amount of interest in the use of the tail conditional expectation (TCE) as a useful measure of risk associated with a production process, for example, in the measurement of risk associated with stock returns corresponding to the manufacturing industry, such as the production of electric bulbs, investment in housing development, and financial institutions offering loans to small-scale industries. Companies typically face three types of risk (and associated losses from each of these sources): strategic (S); operational (O); and financial (F) (insurance companies additionally face insurance risks) and they come from multiple sources. For asymmetric and bounded losses (properly adjusted as necessary) that are continuous in nature, we conjecture that risk assessment measures via univariate/bivariate Kumaraswamy distribution will be efficient in the sense that the resulting TCE based on bivariate Kumaraswamy type copulas do not depend on the marginals. In fact, almost all classical measures of tail dependence are such, but they investigate the amount of tail dependence along the main diagonal of copulas, which has often little in common with the concentration of extremes in the copula’s domain of definition. In this article, we examined the above risk measure in the case of a univariate and bivariate Kumaraswamy (KW) portfolio risk, and computed TCE based on bivariate KW type copulas. For illustrative purposes, a well-known Stock indices data set was re-analyzed by computing TCE for the bivariate KW type copulas to determine which pairs produce minimum risk in a two-component risk scenario.

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“…The models considered in Examples 4 and 5 can be extended by introducing another time change, following the approach of Lin et al (2018). This introduces extra flexibility for, in particular, the final outcome (herd immunity or complete infection).…”

Section: Example 6 : Time-changed Stochastic Processesmentioning

confidence: 99%