A modified pseudo-copula regression model for risk groups with various dependency levels

Statistical actuarial estimation of the Capitation Payment Unit from copula functions and deep learning: historical comparability analysis for the Colombian health system, 2015–2021

“…This statistical technique has been applied in several fields of investigation related to the payment of claims, pricing, active valorization and, with less relevance, stockpile computation, highlighting the opportunity to model the asymmetric dependence in the tails [11,19,20,46,47,51]. More recently, copulas have been applied in collective risk models and deductible price-fixing, furthermore, improvements in the computational efficiency and how to provide intuitive interpretations of the dependence structure have been investigated [13,39,48]. For the sector of health insurance, the applications in the scientific indexed literature have been few [49,54,56], and in that way, this work can also be considered a pioneer in the field.…”

A new algorithmic approach for maximum likelihood estimation of the pseudo-copula regression: P-MBP

“…The comparison of the pseudo-copula regression and the modified pseudo-copula regression models with a simulation study and real data analysis was studied by Erdemir (2020), and the advantages of the modified pseudo-copula regression model were stated. The usefulness of P-MBP for parameter estimation and the assessment of the adequacy of the model demonstrated by Erdemir and Sucu (2021). In this study, only the performances of MBP and P-MBP algorithms were investigated.…”

“…All risk factors are organized as categorical explanatory variables for easy modelling with GLMs and risk classification. The claim severity and frequency are classified according to the level of no claim discount (NCD), the age of vehicle, the engine power and the cause of damage for more effective copula regression modeling (Erdemir 2020;Erdemir and Sucu 2021).…”

“…Besides the advantages of the Gaussian copula function, it is deficient in modeling asymmetric, elliptic and tail dependencies (Brigo et al 2010). The Gaussian copula was developed as the pseudo-Gaussian copula (Fang and Madsen 2013) and the modified pseudo-Gaussian copula (Erdemir and Sucu 2021) to remedy these shortcomings. Let 𝑃𝐶: 𝑰 2 → 𝑰 be a bivariate pseudo-Gaussian copula function for 𝒖 ̂= (𝑢 ̂1, 𝑢 ̂2) ∈ 𝑰 2 pseudo-observations and 𝚪 * = [ 1 𝜌 12 * 𝜌 12 * 1 ] be a modified correlation matrix with a function as 𝜌 12 * = 𝑓(𝑎 12 , 𝑏 12 ; 𝑢 ̂1, 𝑢 ̂2), where 𝑎 12 and 𝑏 12 are the parameters which control the speed at which the model convergences to tail and the tail shape of the model, respectively.…”

An adjusted iterative algorithmic approach for maximum likelihood estimation of the pseudo-copula regression: P-MBP

“…Besides the advantages of the Gaussian copula function, it is deficient in modeling asymmetric, elliptic and tail dependencies (Brigo et al 2010). The Gaussian copula was developed as the pseudo-Gaussian copula (Fang and Madsen 2013) and the modified pseudo-Gaussian copula (Erdemir and Sucu 2021) to remedy these shortcomings. Let 𝑃𝐶: 𝑰 2 → 𝑰 be a bivariate pseudo-Gaussian copula function for 𝒖 ̂= (𝑢 ̂1, 𝑢 ̂2) ∈ 𝑰 2 pseudo-observations and 𝚪 * = [ 1 𝜌 12 * 𝜌 12 * 1 ] be a modified correlation matrix with a function as 𝜌 12 * = 𝑓(𝑎 12 , 𝑏 12 ; 𝑢 ̂1, 𝑢 ̂2), where 𝑎 12 and 𝑏 12 are the parameters which control the speed at which the model convergences to tail and the tail shape of the model, respectively.…”