Stochastic Claims Reserving via a Bayesian Spline Model With Random Loss Ratio Effects

Gao, Guangyuan; Meng, Shengwang

doi:10.1017/asb.2017.19

Cited by 21 publications

(28 citation statements)

References 28 publications

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“…Then the posterior distribution will include estimation of k: Our experience has been that the resulting loo from this ends up close to the lowest loo for any k and can be even slightly lower, possibly due to having an entire posterior distribution of ks. Gao and Meng (2018) did this, and it is done in the mortality example as well.…”

Section: Goodness Of Fit From Mcmcmentioning

confidence: 99%

“…Venter and Şahin (2018) fit the Hunt-Blake mortality model with Bayesian shrinkage of linear splines, determining the shrinkage level by cross-validation. Gao and Meng (2018) used Bayesian shrinkage on cubic splines for loss reserving models, obtaining the shrinkage level by a fully Bayesian method. Here we use linear splines on a Renshaw-Haberman model with a fully Bayesian estimation approach that combines lasso with MCMC to speed convergence.…”

Section: Introductionmentioning

confidence: 99%

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Semiparametric Regression for Dual Population Mortality

Venter

Şahın

2021

North American Actuarial Journal

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Parameter shrinkage applied optimally can always reduce error and projection variances from those of maximum likelihood estimation. Many variables that actuaries use are on numerical scales, like age or year, which require parameters at each point. Rather than shrinking these toward zero, nearby parameters are better shrunk toward each other. Semiparametric regression is a statistical discipline for building curves across parameter classes using shrinkage methodology. It is similar to but more parsimonious than cubic splines. We introduce it in the context of Bayesian shrinkage and apply it to joint mortality modeling for related populations. Bayesian shrinkage of slope changes of linear splines is an approach to semiparametric modeling that evolved in the actuarial literature. It has some theoretical and practical advantages, like closed-form curves, direct and transparent determination of degree of shrinkage and of placing knots for the splines, and quantifying goodness of fit. It is also relatively easy to apply to the many nonlinear models that arise in actuarial work. We find that it compares well to a more complex state-of-the-art statistical spline shrinkage approach on a popular example from that literature.

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Section: Goodness Of Fit From Mcmcmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Semiparametric Regression for Dual Population Mortality

Venter

Şahın

2021

North American Actuarial Journal

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“…A Bayesian formulation of the CL model is provided in Gisler and Wüthrich (2008). More recent examples include Antonio and Beirlant (2008), de Alba and Nieto- Barajas (2008), Peters et al (2009), Meyers (2009), the monograph Meyers (2015), the survey paper Taylor (2015), Gao and Meng (2018), and the recent book Gao (2018). Going down a different route and interpreting the run-off triangles as a spatially organised data set, Lally and Hartman (2018) use Gaussian process regression techniques to estimate the reserves.…”

Section: Introductionmentioning

confidence: 99%

A Gamma Moving Average Process for Modelling Dependence Across Development Years in Run-Off Triangles

Nieto‐Barajas

Targino²

2020

ASTIN Bull.

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We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is based on a gamma process with a moving average form of order $p \ge 0$ which is achieved through the use of poisson latent variables. We carry out Bayesian inference on model parameters and borrow strength across several triangles, coming from different lines of businesses or companies, through the use of hierarchical priors. We carry out a simulation study as well as a real data analysis. Results show that reserve estimates, for the real data set studied, are more accurate with our gamma dependence model as compared to the benchmark over-dispersed poisson that assumes independence.

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“…Venter and Şahin (2017) use a similar approach. A related paper is Gao and Meng (2017), who use Bayesian regularization for cubic spline fitting of an age-cohort model.…”

Section: Introductionmentioning

confidence: 99%

Regularized Age-Period-Cohort Modeling of Opioid Mortality Rates

Venter

2018

AEF

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Opioid mortality rates have been increasing sharply, but not uniformly by age. Peak ages have recently dropped from the mid-40s to the mid-30s. There are two age peaks that have been moving up diagonally, with years of birth around 1960 and 1980 staying near the tops, and those around 1970 generally lower. We model this history with the Lee-Carter plus cohorts mortality model, which includes variable trends by age, and a generalization of it. This can be fit by maximum likelihood estimation (MLE) but statistical methods that shrink parameters towards zero (regularization) give lower predictive variances than MLE does. We address how to apply regularization to age-period-cohort models. Frequentist and Bayesian regularization are explored. The latter has some practical advantages.

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Stochastic Claims Reserving via a Bayesian Spline Model With Random Loss Ratio Effects

Cited by 21 publications

References 28 publications

Semiparametric Regression for Dual Population Mortality

Semiparametric Regression for Dual Population Mortality

A Gamma Moving Average Process for Modelling Dependence Across Development Years in Run-Off Triangles

Regularized Age-Period-Cohort Modeling of Opioid Mortality Rates

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