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 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 (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 (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 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 Financial Time Series Image Algorithm Based on Wavelet Analysis and Data Fusion

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Wuwei Liu ◽  
Jingdong Yan
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Mean Square Error ◽  
Financial Time Series ◽  
Prediction Method ◽  
Mean Square ◽  
Rbf Network ◽  
Network Prediction ◽  
The Mean ◽  
Hidden Layer

In recent years, people are more and more interested in time series modeling and its application in prediction. This paper mainly discusses a financial time series image algorithm based on wavelet analysis and data fusion. In this research, we conducted an in-depth study on the scale decomposition sequence and wavelet transform sequence in different scale domains of wavelet transform according to the scale change rule based on wavelet transform. We use wavelet neural network with different input neurons and hidden neurons to predict, respectively. Finally, the prediction results are integrated into the final prediction results based on the original time series by using wavelet reconstruction technology. Using RBF algorithm in neural network and SPSS Clementine, the wavelet transform sequences on five scales are modeled. Each network model has three layers: one input layer, one hidden layer, and one output layer, and each output layer has only one output element. In order to compare the prediction effect of the model proposed in this study, the ordinary RBF network is used to model and predict the log yield itself. When the input sample is 5, the minimum mean square error is obtained when the hidden layer is 6, and the mean square error is 1.6349. The mean square error of the training phase is 0.0209, and the validation error is 1.6141. The results show that the prediction results of the wavelet prediction method combined with the RBF network prediction method are better than those of wavelet prediction or RBF network prediction.

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 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.

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