Author: Guangyuan Gao
Publisher: Springer
ISBN: 9811336091
Category : Mathematics
Languages : en
Pages : 205
Book Description
This book first provides a review of various aspects of Bayesian statistics. It then investigates three types of claims reserving models in the Bayesian framework: chain ladder models, basis expansion models involving a tail factor, and multivariate copula models. For the Bayesian inferential methods, this book largely relies on Stan, a specialized software environment which applies Hamiltonian Monte Carlo method and variational Bayes.
Bayesian Claims Reserving Methods in Non-life Insurance with Stan
Author: Guangyuan Gao
Publisher: Springer
ISBN: 9811336091
Category : Mathematics
Languages : en
Pages : 205
Book Description
This book first provides a review of various aspects of Bayesian statistics. It then investigates three types of claims reserving models in the Bayesian framework: chain ladder models, basis expansion models involving a tail factor, and multivariate copula models. For the Bayesian inferential methods, this book largely relies on Stan, a specialized software environment which applies Hamiltonian Monte Carlo method and variational Bayes.
Publisher: Springer
ISBN: 9811336091
Category : Mathematics
Languages : en
Pages : 205
Book Description
This book first provides a review of various aspects of Bayesian statistics. It then investigates three types of claims reserving models in the Bayesian framework: chain ladder models, basis expansion models involving a tail factor, and multivariate copula models. For the Bayesian inferential methods, this book largely relies on Stan, a specialized software environment which applies Hamiltonian Monte Carlo method and variational Bayes.
Three Essays on Bayesian Claims Reserving Methods in General Insurance
Author: Guangyuan Gao
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
This thesis investigates the usefulness of Bayesian modelling to claims reserving in general insurance. It can be divided into two parts: Bayesian methodology and Bayesian claims reserving methods. In the first part, we review Bayesian inference and computational methods. Several examples are provided to demonstrate key concepts. Deriving the predictive distribution and incorporating prior information are focused on as two important facets of Bayesian modelling for claims reserving. In the second part, we make the following contributions: 1. Propose a compound model as a stochastic version of the payments per claim incurred method. 2. Introduce the Bayesian basis expansion models and Hamiltonian Monte Carlo method to the claims reserving problem. 3. Use copulas to aggregate the doctor benefit and the hospital benefit in the WorkSafe Victoria scheme. All the Bayesian models proposed are first checked by applying them to simulated data. We estimate the liabilities of outstanding claims arising from the weekly benefit, the doctor benefit and the hospital benefit in the WorkSafe Victoria scheme. We compare our results with those from the PwC report. Except for several Markov chain Monte Carlo algorithms written for the purpose in R and WinBUGS, we largely rely on Stan, a specialized software environment which applies Hamiltonian Monte Carlo method and variational Bayes.
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
This thesis investigates the usefulness of Bayesian modelling to claims reserving in general insurance. It can be divided into two parts: Bayesian methodology and Bayesian claims reserving methods. In the first part, we review Bayesian inference and computational methods. Several examples are provided to demonstrate key concepts. Deriving the predictive distribution and incorporating prior information are focused on as two important facets of Bayesian modelling for claims reserving. In the second part, we make the following contributions: 1. Propose a compound model as a stochastic version of the payments per claim incurred method. 2. Introduce the Bayesian basis expansion models and Hamiltonian Monte Carlo method to the claims reserving problem. 3. Use copulas to aggregate the doctor benefit and the hospital benefit in the WorkSafe Victoria scheme. All the Bayesian models proposed are first checked by applying them to simulated data. We estimate the liabilities of outstanding claims arising from the weekly benefit, the doctor benefit and the hospital benefit in the WorkSafe Victoria scheme. We compare our results with those from the PwC report. Except for several Markov chain Monte Carlo algorithms written for the purpose in R and WinBUGS, we largely rely on Stan, a specialized software environment which applies Hamiltonian Monte Carlo method and variational Bayes.
Full Bayesian Analysis of Claims Reserving Uncertainty
Author: Gareth Peters
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
Book Description
We revisit the gamma-gamma Bayesian chain-ladder (BCL) model for claims reserving in non-life insurance. This claims reserving model is usually used in an empirical Bayesian way using plug-in estimates for variance parameters, because this empirical Bayesian framework allows us for closed form solutions. The main purpose of this paper is to develop the full Bayesian case also considering prior distributions for variance parameters, and to study the resulting sensitivities.
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
Book Description
We revisit the gamma-gamma Bayesian chain-ladder (BCL) model for claims reserving in non-life insurance. This claims reserving model is usually used in an empirical Bayesian way using plug-in estimates for variance parameters, because this empirical Bayesian framework allows us for closed form solutions. The main purpose of this paper is to develop the full Bayesian case also considering prior distributions for variance parameters, and to study the resulting sensitivities.
Claims Reserving in Non-life Insurance
Author: Gregory Clive Taylor
Publisher: North Holland
ISBN:
Category : Business & Economics
Languages : en
Pages : 252
Book Description
Publisher: North Holland
ISBN:
Category : Business & Economics
Languages : en
Pages : 252
Book Description
Bayesian Models for Claims Reserving in Health Insurance
Author: Karin Bühler
Publisher:
ISBN:
Category :
Languages : en
Pages : 82
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 82
Book Description
Contributions to the Theory of Empirical Linear Bayes Estimation and Its Application to Claims Reserving in Non-life Insurance
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Claim Reserving in Non-Life Insurance
Author: G. C. Taylor
Publisher:
ISBN: 9780785542551
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN: 9780785542551
Category :
Languages : en
Pages :
Book Description
Stochastic Loss Reserving Using Generalized Linear Models
Author: Greg Taylor
Publisher:
ISBN: 9780996889704
Category :
Languages : en
Pages : 100
Book Description
In this monograph, authors Greg Taylor and Gráinne McGuire discuss generalized linear models (GLM) for loss reserving, beginning with strong emphasis on the chain ladder. The chain ladder is formulated in a GLM context, as is the statistical distribution of the loss reserve. This structure is then used to test the need for departure from the chain ladder model and to consider natural extensions of the chain ladder model that lend themselves to the GLM framework.
Publisher:
ISBN: 9780996889704
Category :
Languages : en
Pages : 100
Book Description
In this monograph, authors Greg Taylor and Gráinne McGuire discuss generalized linear models (GLM) for loss reserving, beginning with strong emphasis on the chain ladder. The chain ladder is formulated in a GLM context, as is the statistical distribution of the loss reserve. This structure is then used to test the need for departure from the chain ladder model and to consider natural extensions of the chain ladder model that lend themselves to the GLM framework.
Stochastic Claims Reserving Via a Bayesian Spline Model with Random Loss Ratio Effects
Author: Guangyuan Gao
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
We propose a Bayesian spline model which uses a natural cubic B-spline basis with knots placed at every development period to estimate the unpaid claims. Analogous to the smoothing parameter in a smoothing spline, shrinkage priors are assumed for the coefficients of basis functions. The accident period effect is modeled as a random effect, which facilitate the prediction in a new accident period. For model inference, we use Stan to implement the no-U-turn sampler, an automatically tuned Hamiltonian Monte Carlo. The proposed model is applied to the workers' compensation insurance data in the United States. The lower triangle data is used to validate the model.
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
We propose a Bayesian spline model which uses a natural cubic B-spline basis with knots placed at every development period to estimate the unpaid claims. Analogous to the smoothing parameter in a smoothing spline, shrinkage priors are assumed for the coefficients of basis functions. The accident period effect is modeled as a random effect, which facilitate the prediction in a new accident period. For model inference, we use Stan to implement the no-U-turn sampler, an automatically tuned Hamiltonian Monte Carlo. The proposed model is applied to the workers' compensation insurance data in the United States. The lower triangle data is used to validate the model.
Risk Modelling in General Insurance
Author: Roger J. Gray
Publisher: Cambridge University Press
ISBN: 0521863945
Category : Business & Economics
Languages : en
Pages : 409
Book Description
A wide range of topics give students a firm foundation in statistical and actuarial concepts and their applications.
Publisher: Cambridge University Press
ISBN: 0521863945
Category : Business & Economics
Languages : en
Pages : 409
Book Description
A wide range of topics give students a firm foundation in statistical and actuarial concepts and their applications.