22 research outputs found
Credibility for the Chain Ladder Reserving Method
We consider the chain ladder reserving method in a Bayesian set up, which allows for combining the information from a specific claims development triangle with the information from a collective. That is, for instance, to consider simultaneously own company specific data and industry-wide data to estimate the own company's claims reserves. We derive Bayesian estimators and credibility estimators within this Bayesian framework. We show that the credibility estimators are exact Bayesian in the case of the exponential dispersion family with its natural conjugate priors. Finally, we make the link to the classical chain ladder method and we show that using non-informative priors we arrive at the classical chain ladder forecasts. However, the estimates for the mean square error of prediction differ in our Bayesian set up from the ones found in the literature. Hence, the paper also throws a new light upon the estimator of the mean square error of prediction of the classical chain ladder forecasts and suggests a new estimator in the chain ladder metho
A new approach to the credibility formula
The usual credibility formula holds whenever, (i) claim size distribution is a member of the exponential family of distributions, (ii) prior distribution conjugates with claim size distribution, and (iii) square error loss has been considered. As long as, one of these conditions is violent, the usual credibility formula no longer holds. This article, using the mean square error minimization technique, develops a simple and practical approach to the credibility theory. Namely, we approximate the Bayes estimator with respect to a general loss function and general prior distribution by a convex combination of the observation mean and mean of prior, say, approximate credibility formula. Adjustment of the approximate credibility for several situations and its form for several important losses are given.Loss function Balanced loss function Mean square error technique
ESTIMASI PELUANG KEMUNCULAN KLAIM PADA PERUSAHAAN ASURANSI KECELAKAAN MELALUI PEMODELAN POINT PROCESS
Pengajaun klaim pada perusahaan asuransi merupakan kejadian yang terjadi secara acak dan untuk mengantisipasi terjadinya resiko tersebut maka perusahaan asuransi harus mempersiapkan upaya untuk menanggulangi kejadian tersebut dengan memprediksi peluang munculnya klaim. Penelitian ini bertujuan untuk mengestimasi tingkat resiko peluang munculnya klaim dan menentukan peluang munculnya klaim pada interval waktu tertentu. Metode penelitian yang digunakan menggunakan Single Decrement. Data yang digunakan adalah data waktu pengajuan klaim yang terdapat di perusahaan asuransi kecelakaan PT. Jasa Raharja Watampone. Selanjutnya dilakukan pengkonstruksian persamaaan likelihood waktu pengajuan klaim. Data dianalisis secara kuantitatif. Hasil penelitian menunjukkan bahwa tingkat resiko dipengaruhi oleh banyaknya kecelakaan yang terjadi, banyaknya yang mengajukan klaim dan perbandingan rentang waktu pengajuan klaim dari awal interval pengamatan dengan banyaknya hari pada interval waktu pengamatan dan disimpulkan bahwa peluang munculnya klaim pada selang berikutnya akan semakin besar.
Kata kunci: likelihood, single decrement, peluang munculnya klaim, point process, premi, tingkat resiko
Chain ladder method: Bayesian bootstrap versus classical bootstrap
The intention of this paper is to estimate a Bayesian distribution-free chain
ladder (DFCL) model using approximate Bayesian computation (ABC) methodology.
We demonstrate how to estimate quantities of interest in claims reserving and
compare the estimates to those obtained from classical and credibility
approaches. In this context, a novel numerical procedure utilising Markov chain
Monte Carlo (MCMC), ABC and a Bayesian bootstrap procedure was developed in a
truly distribution-free setting. The ABC methodology arises because we work in
a distribution-free setting in which we make no parametric assumptions, meaning
we can not evaluate the likelihood point-wise or in this case simulate directly
from the likelihood model. The use of a bootstrap procedure allows us to
generate samples from the intractable likelihood without the requirement of
distributional assumptions, this is crucial to the ABC framework. The developed
methodology is used to obtain the empirical distribution of the DFCL model
parameters and the predictive distribution of the outstanding loss liabilities
conditional on the observed claims. We then estimate predictive Bayesian
capital estimates, the Value at Risk (VaR) and the mean square error of
prediction (MSEP). The latter is compared with the classical bootstrap and
credibility methods
A new approach to the credibility formula
The usual credibility formula holds whenever, (i) claim size distribution is a member of the exponential
family of distributions, (ii) prior distribution conjugates with claim size distribution, and (iii) square error
loss has been considered. As long as, one of these conditions is violent, the usual credibility formula no
longer holds. This article, using the mean square error minimization technique, develops a simple and
practical approach to the credibility theory. Namely, we approximate the Bayes estimator with respect to
a general loss function and general prior distribution by a convex combination of the observation mean
and mean of prior, say, approximate credibility formula. Adjustment of the approximate credibility for
several situations and its form for several important losses are given
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Reversible jump Markov chain Monte Carlo method for parameter reduction in claims reserving
We present an application of the reversible jump Markov chain Monte Carlo (RJMCMC) method to the important problem of setting claims reserves in general insurance business for the outstanding loss liabilities. A measure of the uncertainty in these claims reserves estimates is also needed for solvency purposes. The RJMCMC method described in this paper represents an improvement over the manual processes often employed in practice. In particular, our RJMCMC method describes parameter reduction and tail factor estimation in the claims reserving process, and, moreover, it provides the full predictive distribution of the outstanding loss liabilities
Higher Moments of the Claims Development Result in General Insurance
The claims development result (CDR) is one of the major risk drivers in the profit and loss statement of a general insurance company. Therefore, the CDR has become a central object of interest under new solvency regulation. In current practice, simple methods based on the first two moments of the CDR are implemented to find a proxy for the distribution of the CDR. Such approximations based on the first two moments are rather rough and may fail to appropriately describe the shape of the distribution of the CDR. In this paper we provide an analysis of higher moments of the CDR. Within a Bayes chain ladder framework we consider two different models for which it is possible to derive analytical solutions for the higher moments of the CDR. Based on higher moments we can e.g. calculate the skewness and the excess kurtosis of the distribution of the CDR and obtain refined approximations. Moreover, a case study investigates and answers questions raised in IAS