scholarly journals The Prediction Error of the Chain Ladder Method (With Application to Real Data)

2020 ◽  
Vol 12 (12) ◽  
pp. 14
Author(s):  
Afaf Antar Zohry ◽  
Mostafa Abdelghany Ahmed
Keyword(s):  
Prediction Error ◽  
Real Data ◽  
Solvency Ii ◽  
Insurance Companies ◽  
Mean Square ◽  
Recursive Model ◽  
Chain Ladder Method ◽  
The Mean ◽  
Chain Ladder ◽  
S Model

The chain ladder method is the most widely used method of estimating claims reserves due to its simplicity and ease of application. It is very important to know the accuracy of the resulting estimates. Murphy presented a recursive model to estimate the standard error of claims reserves estimates, in line with the solvency ii requirements as a new regulatory framework adjusted according to risk, which requires the necessity to estimate the error and uncertainty of the claims reserving estimates. In Murphy's model, the mean square error (MSE) is analyzed into its components: variance and bias. In this paper, the recursive model of Murphy was used to estimate the prediction error in claims reserves estimates of General Accident & Miscellaneous Insurance in one of the Egyptian insurance companies.

scholarly journals Prediction Error of the Chain Ladder Reserving Method applied to Correlated Run-off Triangles

2007 ◽  
Vol 2 (1) ◽  
pp. 25-50 ◽  
Author(s):  
M. Merz ◽  
M. V. Wüthrich
Keyword(s):  
Time Series ◽  
Mean Square Error ◽  
Prediction Error ◽  
Time Series Model ◽  
Mean Square ◽  
Run Off ◽  
Chain Ladder Method ◽  
The Mean ◽  
Chain Ladder ◽  
Special Case

ABSTRACTIn Buchwalder et al. (2006) we revisited Mack's (1993) and Murphy's (1994) estimates for the mean square error of prediction (MSEP) of the chain ladder claims reserving method. This was done using a time series model for the chain ladder method. In this paper we extend the time series model to determine an estimate for the MSEP of a portfolio of N correlated run-off triangles. This estimate differs in the special case N = 2 from the estimate given by Braun (2004). We discuss the differences between the estimates.

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

2006 ◽  
Vol 36 (2) ◽  
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 Credibility for the Chain Ladder Reserving Method

2008 ◽  
Vol 38 (2) ◽  
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 Fiscal Marksmanship in Pakistan

2010 ◽  
Vol 15 (2) ◽  
pp. 113-133 ◽  
Author(s):  
Muhammad Zakaria ◽  
Shujat Ali
Keyword(s):  
Prediction Error ◽  
Rational Expectations ◽  
Central Government ◽  
Mean Square ◽  
Government Budget ◽  
Exogenous Variables ◽  
Random Components ◽  
The Mean ◽  
Source Of Error ◽  
Over Time

Using Theil’s inequality coefficient based on the mean square prediction error, this paper evaluates the forecasting efficiency of the central government budget and revised budget estimates in Pakistan for the period 1987/88 to 2007/08 and decomposes the errors into biasedness, unequal variation and random components to analyze the source of error. The results reveal that budgetary forecasting is inefficient in Pakistan and the error is due mainly to exogenous variables (random factors). We also find that neither the budget nor revised budget estimates of revenue and expenditure satisfy the criteria of rational expectations of forecasting. Further, there is very little evidence of improvement in the efficiency of budgetary forecasts over time.

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 Neural Networks for the Joint Development of Individual Payments and Claim Incurred

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 33
Author(s):  
Łukasz Delong ◽  
Mario V. Wüthrich
Keyword(s):  
Neural Networks ◽  
Regression Models ◽  
Development Process ◽  
Real Data ◽  
Data Set ◽  
Joint Development ◽  
Chain Ladder Method ◽  
History Of ◽  
Feature Information ◽  
Chain Ladder

The goal of this paper is to develop regression models and postulate distributions which can be used in practice to describe the joint development process of individual claim payments and claim incurred. We apply neural networks to estimate our regression models. As regressors we use the whole claim history of incremental payments and claim incurred, as well as any relevant feature information which is available to describe individual claims and their development characteristics. Our models are calibrated and tested on a real data set, and the results are benchmarked with the Chain-Ladder method. Our analysis focuses on the development of the so-called Reported But Not Settled (RBNS) claims. We show benefits of using deep neural network and the whole claim history in our prediction problem.

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).

Sign in / Sign up

Export Citation Format

Share Document