Deriving Robust Bayesian Premiums Under Bands of Prior Distributions With Applications

Sánchez-Sánchez, Marta; Sordo, Miguel Á.; Suárez‐Llorens, Alfonso; Gómez–Déniz, Emilio

doi:10.1017/asb.2018.36

Cited by 7 publications

(5 citation statements)

References 35 publications

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“…To conclude, applying our method to the province of Cádiz, located at the South of Spain, we were able to discuss the effectiveness of the first lockdown, the accuracy of the estimates during that lockdown and the beginning of the second and third waves after the lockdown. For future works it would be interesting to apply robust Bayesian techniques as described in [46][47][48][49]. In particular, it would be interesting to consider a band of prior distributions for the parameter a as described in [46].…”

Section: Discussionmentioning

confidence: 99%

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

Sánchez-Sánchez

Suárez‐Llorens

2021

Mathematics

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The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an intensity function based on the Gompertz curve. We discuss the prior distribution of the parameter and we generate samples from the posterior distribution by using Markov Chain Monte Carlo (MCMC) methods. Finally, we illustrate our method analyzing real data associated with COVID-19 in a specific region located at the south of Spain.

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Section: Discussionmentioning

confidence: 99%

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

Sánchez-Sánchez

Suárez‐Llorens

2021

Mathematics

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“…2. Applying Remark 8 in Sánchez-Sánchez et al (2019) and Corollaries 1 and 2 we obtain that for every there exists ∈ Γ , , such that is equal to the Bayes estimator with respect to the prior .…”

Section: Lemma 1 Let Be An Increasing Function Of Letmentioning

confidence: 99%

“…The family considered in the paper can be an alternative. In insurance this class was considered by Sánchez-Sánchez et al (2019). The concept of distortion functions has been used in actuarial science to model risk measure (see, for example, Balbas et al (2009)).…”

Section: Introductionmentioning

confidence: 99%

Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss

Boratyńska

2021

Statistics in Transition New Series

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The article presents a collective risk model for the insurance claims. The objective is to estimate a premium, which is defined as a functional specified up to unknown parameters. For this purpose, the Bayesian methodology, which combines the prior knowledge about certain unknown parameters with the knowledge in the form of a random sample, has been adopted. The generalised Bregman loss function is considered. In effect, the results can be applied to numerous loss functions, including the square-error, LINEX, weighted squareerror, Brown, entropy loss. Some uncertainty about a prior is assumed by a distorted band class of priors. The range of collective and Bayes premiums is calculated and posterior regret Γ-minimax premium as a robust procedure has been implemented. Two examples are provided to illustrate the issues considered -the first one with an unknown parameter of the Poisson distribution, and the second one with unknown parameters of distributions of the number and severity of claims.

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“…Furthermore, since we are not sure whether the naive prior or the proposed prior represents true dynamics on θ, we consider the family of distribution Q which has the average of standard deviations of θ under the naive and proposed priors as the standard deviation of θ with q(θ). One can see that there are some research works which specified the class Q in terms of moments, including but not limited to Eichenauer et al (1988), Young (1998), Insua et al (1999), Gómez-Déniz et al (2002a, Boratyńska (2017), andSánchez-Sánchez et al (2019).…”

Section: Bayesian Sensitivity Analysis With Bregman Divergencementioning

confidence: 99%

Testing for Random Effects in Compound Risk Models via Bregman Divergence

Jeong¹

2020

ASTIN Bull.

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Abstract The generalized linear model (GLM) is a statistical model which has been widely used in actuarial practices, especially for insurance ratemaking. Due to the inherent longitudinality of property and casualty insurance claim datasets, there have been some trials of incorporating unobserved heterogeneity of each policyholder from the repeated observations. To achieve this goal, random effects models have been proposed, but theoretical discussions of the methods to test the presence of random effects in GLM framework are still scarce. In this article, the concept of Bregman divergence is explored, which has some good properties for statistical modeling and can be connected to diverse model selection diagnostics as in Goh and Dey [(2014) Journal of Multivariate Analysis, 124, 371–383]. We can apply model diagnostics derived from the Bregman divergence for testing robustness of a chosen prior by the modeler to possible misspecification of prior distribution both on the naive model, which assumes that random effects follow a point mass distribution as its prior distribution, and the proposed model, which assumes a continuous prior density of random effects. This approach provides insurance companies a concrete framework for testing the presence of nonconstant random effects in both claim frequency and severity and furthermore appropriate hierarchical model which can explain both observed and unobserved heterogeneity of the policyholders for insurance ratemaking. Both models are calibrated using a claim dataset from the Wisconsin Local Government Property Insurance Fund which includes both observed claim counts and amounts from a portfolio of policyholders.

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Deriving Robust Bayesian Premiums Under Bands of Prior Distributions With Applications

Cited by 7 publications

References 35 publications

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

Robust Bayesian insurance premium in a collective risk model with distorted priors under the generalised Bregman loss

Testing for Random Effects in Compound Risk Models via Bregman Divergence

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