scholarly journals Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method

2009 ◽  
Vol 4 (1) ◽  
pp. 7-31 ◽  
Author(s):  
D. H. Alai ◽  
M. Merz ◽  
M. V. Wüthrich
Keyword(s):  
Mean Square Error ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Poisson Model ◽  
Development Pattern ◽  
Mean Square ◽  
Conditional Mean ◽  
Major Subject ◽  
Chain Ladder

ABSTRACTThe prediction of adequate claims reserves is a major subject in actuarial practice and science. Due to their simplicity, the chain ladder (CL) and Bornhuetter–Ferguson (BF) methods are the most commonly used claims reserving methods in practice. However, in contrast to the CL method, no estimator for the conditional mean square error of prediction (MSEP) of the ultimate claim has been derived in the BF method until now, and as such, this paper aims to fill that gap. This will be done in the framework of generalized linear models (GLM) using the (overdispersed) Poisson model motivation for the use of CL factor estimates in the estimation of the claims development pattern.

Prediction Uncertainty in the Bornhuetter-Ferguson Claims Reserving Method: Revisited

2010 ◽  
Vol 5 (1) ◽  
pp. 7-17 ◽  
Author(s):  
D. H. Alai ◽  
M. Merz ◽  
M. V. Wüthrich
Keyword(s):  
Maximum Likelihood ◽  
Stochastic Model ◽  
Mean Square Error ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Maximum Likelihood Estimators ◽  
Model Parameters ◽  
Mean Square ◽  
Conditional Mean ◽  
Prediction Uncertainty

AbstractWe revisit the stochastic model of Alai et al. (2009) for the Bornhuetter-Ferguson claims reserving method, Bornhuetter & Ferguson (1972). We derive an estimator of its conditional mean square error of prediction (MSEP) using an approach that is based on generalized linear models and maximum likelihood estimators for the model parameters. This approach leads to simple formulas, which can easily be implemented in a spreadsheet.

scholarly journals Prediction uncertainties in the Cape Cod reserving method

2015 ◽  
Vol 9 (2) ◽  
pp. 239-263 ◽  
Author(s):  
Annina Saluz
Keyword(s):  
Stochastic Model ◽  
Mean Square Error ◽  
Cape Cod ◽  
Parameter Estimates ◽  
Mean Square ◽  
Established Method ◽  
Distribution Free ◽  
Conditional Mean ◽  
Chain Ladder ◽  
Development Result

AbstractThe Cape Cod (CC) method was designed by Bühlmann and Straub in order to overcome some shortcomings of the chain ladder (CL) method. Owing to its simplicity and because of the advantages over the CL method, the CC method has become a well-established method in practice. In this paper we consider a distribution-free stochastic model for the CC method. Within this model we give the parameter estimates and we derive estimates for the conditional mean square error of prediction for the CC method. In addition, we derive an estimate for the uncertainty in the claims development result.

scholarly journals Taylor Approximations for Model Uncertainty within the Tweedie Exponential Dispersion Family

2009 ◽  
Vol 39 (2) ◽  
pp. 453-477 ◽  
Author(s):  
Daniel H. Alai ◽  
Mario V. Wüthrich
Keyword(s):  
Case Studies ◽  
Mean Square Error ◽  
Generalized Linear Models ◽  
Standard Method ◽  
Model Uncertainty ◽  
Linear Models ◽  
Mean Square ◽  
Multiple Case ◽  
Multiple Case Studies ◽  
Tweedie Family

AbstractThe use of generalized linear models (GLM) to estimate claims reserves has become a standard method in insurance. Most frequently, the exponential dispersion family (EDF) is used; see e.g. England, Verrall. We study the so-called Tweedie EDF and test the sensitivity of the claims reserves and their mean square error of predictions (MSEP) over this family. Furthermore, we develop second order Taylor approximations for the claims reserves and the MSEPs for members of the Tweedie family that are difficult to obtain in practice, but are close enough to models for which claims reserves and MSEP estimations are easy to determine. As a result of multiple case studies, we find that claims reserves estimation is relatively insensitive to which distribution is chosen amongst the Tweedie family, in contrast to the MSEP, which varies widely.

scholarly journals The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)

2006 ◽  
Vol 36 (02) ◽  
pp. 521-542 ◽  
Author(s):  
Markus Buchwalder ◽  
Hans Bühlmann ◽  
Michael Merz ◽  
Mario V. Wüthrich
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Time Series Model ◽  
Mean Square ◽  
Chain Ladder Method ◽  
The Mean ◽  
Chain Ladder

We revisit the famous Mack formula [2], which gives an estimate for the mean square error of prediction MSEP of the chain ladder claims reserving method: We define a time series model for the chain ladder method. In this time series framework we give an approach for the estimation of the conditional MSEP. It turns out that our approach leads to results that differ from the Mack formula. But we also see that our derivation leads to the same formulas for the MSEP estimate as the ones given in Murphy [4]. We discuss the differences and similarities of these derivations.

scholarly journals The Mean Square Error of Prediction in the Chain Ladder Reserving Method – A Comment

2006 ◽  
Vol 36 (02) ◽  
pp. 543-552 ◽  
Author(s):  
Thomas Mack ◽  
Gerhard Quarg ◽  
Christian Braun
Keyword(s):  
Mean Square Error ◽  
Negative Correlation ◽  
Mean Square ◽  
New Approach ◽  
The Mean ◽  
Chain Ladder ◽  
Original Formula

We discuss some questionable points of the approach taken in the paper by Buchwalder, Bühlmann, Merz and Wüthrich and come to the conclusion that this approach does not yield an improvement of Mack’s original formula. The main reason is that the new approach disregards the negative correlation of the squares of the development factors. The same applies to the formula by Murphy (PCAS 1994).

scholarly journals The Mean Square Error of Prediction in the Chain Ladder Reserving Method – A Comment

2006 ◽  
Vol 36 (2) ◽  
pp. 543-552 ◽  
Author(s):  
Thomas Mack ◽  
Gerhard Quarg ◽  
Christian Braun
Keyword(s):  
Mean Square Error ◽  
Negative Correlation ◽  
Mean Square ◽  
New Approach ◽  
The Mean ◽  
Chain Ladder ◽  
Original Formula

We discuss some questionable points of the approach taken in the paper by Buchwalder, Bühlmann, Merz and Wüthrich and come to the conclusion that this approach does not yield an improvement of Mack’s original formula. The main reason is that the new approach disregards the negative correlation of the squares of the development factors. The same applies to the formula by Murphy (PCAS 1994).

scholarly journals Credibility for the Chain Ladder Reserving Method

2008 ◽  
Vol 38 (02) ◽  
pp. 565-600 ◽  
Author(s):  
Alois Gisler ◽  
Mario V. Wüthrich
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Specific Data ◽  
Conjugate Priors ◽  
Chain Ladder Method ◽  
The Mean ◽  
Chain Ladder ◽  
Set Up ◽  
Classical Chain ◽  
Development Triangle

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 method.

scholarly journals Overdispersed-Poisson Model in Claims Reserving: Closed Tool for One-Year Volatility in GLM Framework

Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 139
Author(s):  
Stefano Strascia ◽  
Agostino Tripodi
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Poisson Model ◽  
Point Of View ◽  
Approximation Techniques ◽  
The Monte Carlo Method ◽  
Calculation Point ◽  
One Year ◽  
The One ◽  
Bootstrap Methodology

The aim of this paper is to carry out a closed tool to estimate the one-year volatility of the claims reserve, calculated through the generalized linear models (GLM), notably the overdispersed- Poisson model. Up to now, this one-year volatility has been estimated through the well-known bootstrap methodology that demands the use of the Monte Carlo method with a re-reserving technique. Nonetheless, this method is time consuming under the calculation point of view; therefore, approximation techniques are often used in practice, such as an emergence pattern based on the link between the one-year volatility—resulting from the Merz–Wüthrich method—and the ultimate volatility—resulting from the Mack method.

Sign in / Sign up

Export Citation Format

Share Document