Bayesian Claims Reserving Methods in Non-life Insurance with Stan PDF Download
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Author: Guangyuan Gao
Publisher: Springer
ISBN: 9811336091
Category : Mathematics
Languages : en
Pages : 205
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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.
Author: Guangyuan Gao
Publisher: Springer
ISBN: 9811336091
Category : Mathematics
Languages : en
Pages : 205
Get Book Here
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.
Author: Guangyuan Gao
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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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.
Author: Gareth Peters
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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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.
Author: Gregory Clive Taylor
Publisher: North Holland
ISBN:
Category : Business & Economics
Languages : en
Pages : 252
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Book Description
Author: Greg Taylor
Publisher:
ISBN: 9780996889704
Category :
Languages : en
Pages : 100
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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.
Author: Mario V. Wüthrich
Publisher: John Wiley & Sons
ISBN: 0470772727
Category : Business & Economics
Languages : en
Pages : 438
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Book Description
Claims reserving is central to the insurance industry. Insurance liabilities depend on a number of different risk factors which need to be predicted accurately. This prediction of risk factors and outstanding loss liabilities is the core for pricing insurance products, determining the profitability of an insurance company and for considering the financial strength (solvency) of the company. Following several high-profile company insolvencies, regulatory requirements have moved towards a risk-adjusted basis which has lead to the Solvency II developments. The key focus in the new regime is that financial companies need to analyze adverse developments in their portfolios. Reserving actuaries now have to not only estimate reserves for the outstanding loss liabilities but also to quantify possible shortfalls in these reserves that may lead to potential losses. Such an analysis requires stochastic modeling of loss liability cash flows and it can only be done within a stochastic framework. Therefore stochastic loss liability modeling and quantifying prediction uncertainties has become standard under the new legal framework for the financial industry. This book covers all the mathematical theory and practical guidance needed in order to adhere to these stochastic techniques. Starting with the basic mathematical methods, working right through to the latest developments relevant for practical applications; readers will find out how to estimate total claims reserves while at the same time predicting errors and uncertainty are quantified. Accompanying datasets demonstrate all the techniques, which are easily implemented in a spreadsheet. A practical and essential guide, this book is a must-read in the light of the new solvency requirements for the whole insurance industry.
Author: Roger J. Gray
Publisher: Cambridge University Press
ISBN: 0521863945
Category : Business & Economics
Languages : en
Pages : 409
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Book Description
A wide range of topics give students a firm foundation in statistical and actuarial concepts and their applications.
Author: Mark R. Shapland
Publisher:
ISBN: 9780996889742
Category : Actuarial science
Languages : en
Pages : 116
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Book Description
Author: Dani Gamerman
Publisher: CRC Press
ISBN: 148229642X
Category : Mathematics
Languages : en
Pages : 342
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Book Description
While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, Markov Chain Monte Carlo: Stochastic Simul
Author: Mark Goldburd
Publisher:
ISBN: 9780996889728
Category :
Languages : en
Pages : 106
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Book Description
