A GLM Approach to Estimating Copula Models

Najafabadi, Amir T. Payandeh; Qazvini, Marjan

doi:10.1080/03610918.2013.824588

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…[14]. A copula quantile regression approach was used to estimate the parameters of copula [15]. In this study, it is examined how the estimates will change if the dependency between the claim severity and frequency is considered instead of the independence assumption, which is frequently used in nonlife insurance mathematics.…”

Section: Introductionmentioning

confidence: 99%

The Incorporation of Generalized Linear Models into Bivariate Gaussian Copula and An Application

Erdemir

Sucu

2022

İstatistik Ve Uygulamalı Bilimler Dergisi

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In non-life insurance mathematics, analyses and premium or reserve calculations are carried out in the presence of dependency between the claim variables in recent years. And, thus over- or underestimation of aggregate loss caused by the assumption of dependency between the claim severity and frequency are prevented. The Gaussian copula function, which is frequently used for dependency modeling, is integrated into the marginal generalized linear models to obtain a mixed copula-based regression model called "copula regression". In this study, a copula regression model is created using a bivariate Gaussian copula, Gamma and Poisson marginal generalized linear models for claim severity and frequency, respectively. An application is performed with a simulated data where there is a dependence between the claim severity and frequency using the R package “CopulaRegression”. The importance of the modeling of dependency between claims is investigated by the comparison of the independent and dependent models and the results of application show that the copula regression model in which dependency is considered has lower relative mean square errors compared the independent marginal generalized linear models.

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Section: Introductionmentioning

confidence: 99%

The Incorporation of Generalized Linear Models into Bivariate Gaussian Copula and An Application

Erdemir

Sucu

2022

İstatistik Ve Uygulamalı Bilimler Dergisi

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“…(2016) showed that in a situation that the premium budget is not sufficiently high enough, under the CVaR optimality criteria, the optimal reinsurance policy will change from the stop-loss contract to a one-layer stop-loss. Payandeh Najafabadi & Panahi Bazaz (2016) considered a co-reinsurance contract which is a combination of several reinsurance contracts. Using a Bayesian approach parameters of co-reinsurance contract have been estimated.…”

Section: Introductionmentioning

confidence: 99%

An optimal multi-layer reinsurance policy under conditional tail expectation

Najafabadi

Bazaz

2017

Ann. actuar. sci.

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A usual reinsurance policy for insurance companies admits one or two layers of the payment deductions. Under optimal criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer's total risk, this article generalized an optimal stop-loss reinsurance policy to an optimal multi-layer reinsurance policy. To achieve such optimal multi-layer reinsurance policy, this article starts from a given optimal stop-loss reinsurance policy f (·). In the first step, it cuts down an interval [0, ∞) into two intervals [0, M 1 ) and [M 1 , ∞). By shifting the origin of Cartesian coordinate system to (M 1 , f (M 1 )), and showing that under the CT E criteriais, again, an optimal policy. This extension procedure can be repeated to obtain an optimal k-layer reinsurance policy. Finally, unknown parameters of the optimal multi-layer reinsurance policy are estimated using some additional appropriate criteria. Three simulation-based studies have been conducted to demonstrate: (1) The practical applications of our findings and (2) How one may employ other appropriate criteria to estimate unknown parameters of an optimal multi-layer contract. The multi-layer reinsurance policy, similar to the original stop-loss reinsurance policy is optimal, in a same sense. Moreover it has some other optimal criteria which the original policy does not have. Under optimal criterion of minimizing general translative and monotone risk measure ρ(·) of either the insurer's total risk or both the insurer's and the reinsurer's total risks, this article (in its discussion) also extends a given optimal reinsurance contract f (·) to a multi-layer and continuous reinsurance policy.

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An optimal co-reinsurance strategy

Najafabadi

Bazaz

2016

Insurance: Mathematics and Economics

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A GLM Approach to Estimating Copula Models

Cited by 3 publications

References 11 publications

The Incorporation of Generalized Linear Models into Bivariate Gaussian Copula and An Application

The Incorporation of Generalized Linear Models into Bivariate Gaussian Copula and An Application

An optimal multi-layer reinsurance policy under conditional tail expectation

An optimal co-reinsurance strategy

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