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Journal articles on the topic 'Chain-ladder method'

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Published: 4 June 2021
Last updated: 25 April 2022

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1

Merz, Michael, and Mario Wüthrich. "Modified Munich Chain-Ladder Method." Risks 3, no. 4 (December 21, 2015): 624–46. http://dx.doi.org/10.3390/risks3040624.

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2

Gabrielli, Andrea, and Mario V. Wüthrich. "Back-testing the chain-ladder method." Annals of Actuarial Science 13, no. 2 (November 13, 2018): 334–59. http://dx.doi.org/10.1017/s1748499518000325.

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AbstractThe chain-ladder method is one of the most popular claims reserving techniques. The aim of this study is to back-test the chain-ladder method. For this purpose, we use a stochastic scenario generator that allows us to simulate arbitrarily many upper claims reserving triangles of similar characteristics for which we also know the corresponding lower triangles. Based on these simulated triangles, we analyse the performance of the chain-ladder claims reserving method.
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3

Gisler, Alois, and Mario V. Wüthrich. "Credibility for the Chain Ladder Reserving Method." ASTIN Bulletin 38, no. 02 (November 2008): 565–600. http://dx.doi.org/10.2143/ast.38.2.2033354.

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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.
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4

Gisler, Alois, and Mario V. Wüthrich. "Credibility for the Chain Ladder Reserving Method." ASTIN Bulletin 38, no. 2 (November 2008): 565–600. http://dx.doi.org/10.1017/s0515036100015294.

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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.
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5

Dina Manolache, Aurora Elena. "Chain claims reserving methods in non-life insurance." Proceedings of the International Conference on Applied Statistics 1, no. 1 (October 1, 2019): 216–25. http://dx.doi.org/10.2478/icas-2019-0019.

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Abstract Considering that the reliability of reserves valuation directly influences the financial strength of an insurance company, the main aim of this paper is to present a claims reserving estimation for a Romanian non-life insurer based on the most popular chain methods which are typically used in practice for the estimation of outstanding claims reserves in general insurance industry: Standard Chain Ladder and Munich Chain Ladder both on the claims incurred data and claims paid data. The tail development factors have been estimated based on the curve-fitting methods. The obvious advantage of these methods is represented by its simplicity of the practicality application. The results of the research under two chain claims reserving models reveal significant differences between the Standard Chain Ladder and Munich Chain Ladder with respect to the claims reserves level. Probably the Standard Chain Ladder based on paid method underestimates the outstanding loss liabilities and Standard Chain Ladder based on Incurred method overestimates the claims reserves. The claims reserves predictions under the Paid Munich Chain Ladder and Incurred Munich Chain Ladder are between the two Standard Chain Ladder outstanding loss liabilities estimates. The results of the tail extrapolation shown that the incorporation of the tail factors can have a significant impact on claims predictions.
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6

Van Wouwe, Martine, and Nattakorn Phewchean. "Robustifying the multivariate chain-ladder method: A comparison of two methods." Journal of Governance and Regulation 5, no. 1 (2016): 70–77. http://dx.doi.org/10.22495/jgr_v5_i1_p9.

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The expected result of a non-life insurance company is usually determined for its activity in different business lines as a whole. This implies that the claims reserving problem for a portfolio of several (perhaps correlated) subportfolios is to be solved. A popular technique for studying such a portfolio is the chain-ladder method. However, it is well known that the chain-ladder method is very sensitive to outlying data. For the bivariate situation, we have already developed robust solutions for the chain-ladder method by introducing two techniques for detecting and correcting outliers. In this article we focus on higher dimensions. Being subjected to multiple constraints (no graphical plots available), the goal of our research is to find solutions to detect and smooth the influence of outlying data on the outstanding claims reserve in higher dimensional data sets. The methodologies are illustrated and computed for real examples from the insurance practice.
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7

Hiabu, M., C. Margraf, M. D. Martínez-Miranda, and J. P. Nielsen. "The link between classical reserving and granular reserving through double chain ladder and its extensions." British Actuarial Journal 21, no. 01 (October 22, 2015): 97–116. http://dx.doi.org/10.1017/s1357321715000288.

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AbstractThe relationship of the chain ladder method to mathematical statistics has long been debated in actuarial science. During the 1990s it became clear that the originally deterministic chain ladder can be seen as an autoregressive time series or as a multiplicative Poisson model. This paper draws on recent research and concludes that chain ladder can be seen as a structured histogram. This gives a direct link between classical aggregate methods and continuous granular methods. When the histogram is replaced by a smooth counterpart, we have a continuous chain ladder model. Re-inventing classical chain ladder via double chain ladder and its extensions introduces statistically solid approaches of combining paid and incurred data with direct link to granular data approaches. This paper goes through some of the extensions of double chain ladder and introduces new approaches to incorporating and modelling incurred data.
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8

Schmidt, Klaus D., and Anja Schnaus. "An Extension of Mack's Model for the Chain Ladder Method." ASTIN Bulletin 26, no. 2 (November 1996): 247–62. http://dx.doi.org/10.2143/ast.26.2.563223.

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AbstractThe chain ladder method is a simple and suggestive tool in claims reserving, and various attempts have been made aiming at its justification in a stochastic model. Remarkable progress has been achieved by Schnieper and Mack who considered models involving assumptions on conditional distributions. The present paper extends the model of Mack and proposes a basic model in a decision theoretic setting. The model allows to characterize optimality of the chain ladder factors as predictors of non-observable development factors and hence optimality of the chain ladder predictors of aggregate claims at the end of the first non-observable calendar year. We also present a model in which the chain ladder predictor of ultimate aggregate claims turns out to be unbiased.
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9

Verdonck, Tim, Martine Van Wouwe, and Jan Dhaene. "A Robustification of the Chain-Ladder Method." North American Actuarial Journal 13, no. 2 (April 2009): 280–98. http://dx.doi.org/10.1080/10920277.2009.10597555.

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10

Dahms, René. "CHAIN-LADDER METHOD AND MIDYEAR LOSS RESERVING." ASTIN Bulletin 48, no. 1 (March 28, 2017): 3–24. http://dx.doi.org/10.1017/asb.2017.1.

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AbstractAlthough loss reserving has been deeply studied in the literature, there are still practical issues that have not been addressed a lot. One of them is the estimation of reserves during the year, which is necessary for forecasts or closings during the year. We will study the following question: What can be done for forecasts and closings during the year that goes along with the reserving at year end? In order to make it not too complicated, we will focus on the Chain-Ladder method introduced by Mack (1993). We will describe several methods that are used in practice. We will discuss advantages and disadvantages of these methods based on a simple deterministic example. Roughly spoken, we will see that you may shift development or accident periods, or may split development periods, but should not split accident periods.
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11

Peremans, Kris, Stefan Van Aelst, and Tim Verdonck. "A Robust General Multivariate Chain Ladder Method." Risks 6, no. 4 (September 30, 2018): 108. http://dx.doi.org/10.3390/risks6040108.

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The chain ladder method is a popular technique to estimate the future reserves needed to handle claims that are not fully settled. Since the predictions of the aggregate portfolio (consisting of different subportfolios) do not need to be equal to the sum of the predictions of the subportfolios, a general multivariate chain ladder (GMCL) method has already been proposed. However, the GMCL method is based on the seemingly unrelated regression (SUR) technique which makes it very sensitive to outliers. To address this issue, we propose a robust alternative that estimates the SUR parameters in a more outlier resistant way. With the robust methodology it is possible to automatically flag the claims with a significantly large influence on the reserve estimates. We introduce a simulation design to generate artificial multivariate run-off triangles based on the GMCL model and illustrate the importance of taking into account contemporaneous correlations and structural connections between the run-off triangles. By adding contamination to these artificial datasets, the sensitivity of the traditional GMCL method and the good performance of the robust GMCL method is shown. From the analysis of a portfolio from practice it is clear that the robust GMCL method can provide better insight in the structure of the data.
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12

Wüthrich, Mario V. "Prediction error in the chain ladder method." Insurance: Mathematics and Economics 42, no. 1 (February 2008): 378–88. http://dx.doi.org/10.1016/j.insmatheco.2007.05.002.

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13

Verrall, R. J. "A state space representation of the chain ladder linear model." Journal of the Institute of Actuaries 116, no. 3 (December 1989): 589–609. http://dx.doi.org/10.1017/s0020268100036714.

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In a recent paper, Kremer (1982) has shown how the classical chain ladder method for estimating outstanding claims on general insurance business is strongly related to a two-way analysis of variance. It can be argued that the estimation methods in a standard chain ladder analysis are inefficient from a statistical viewpoint and that an analysis of variance is more appropriate. Once the chain ladder method is identified with a standard statistical method, the well-known statistical theory can be used to the advantage of the claims reserver. For a further discussion of the use of main stream statistical theory applied to the least squares estimation of the linear model which is close to the chain ladder method, the reader is referred to Renshaw (1989).
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14

Röhr, Ancus. "CHAIN LADDER AND ERROR PROPAGATION." ASTIN Bulletin 46, no. 2 (April 19, 2016): 293–330. http://dx.doi.org/10.1017/asb.2016.9.

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AbstractWe show how estimators for the chain ladder prediction error in Mack's (1993) distribution-free stochastic model can be derived using the error propagation formula. Our method allows for the treatment of the general case of the prediction error of the loss development result between two arbitrary future horizons. In the well-known special cases considered previously by Mack (1993) and Merz and Wüthrich (2008), our estimators coincide with theirs. However, the algebraic form in which we cast them is new, considerably more compact and more intuitive to understand. For example, in the classical case treated by Mack (1993), we show that the mean squared prediction error divided by the squared estimated ultimate loss can be written as ∑jû2j, where ûj measures the (relative) uncertainty around the jth development factor and the proportion of the estimated ultimate loss that it affects. The error propagation method also provides a natural split into process error and parameter error. Our proofs identify and exploit symmetries of “chain ladder processes” in a novel way. For the sake of wider practical applicability of the formulae derived, we allow for incomplete historical data and the exclusion of outliers in the triangles.
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15

Schmidt, Klaus D. "Non-optimal prediction by the chain ladder method." Insurance: Mathematics and Economics 21, no. 1 (October 1997): 17–24. http://dx.doi.org/10.1016/s0167-6687(97)00015-2.

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16

Peremans, Kris, Pieter Segaert, Stefan Van Aelst, and Tim Verdonck. "Robust bootstrap procedures for the chain-ladder method." Scandinavian Actuarial Journal 2017, no. 10 (December 9, 2016): 870–97. http://dx.doi.org/10.1080/03461238.2016.1263236.

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17

Peters, Gareth W., Mario V. Wüthrich, and Pavel V. Shevchenko. "Chain ladder method: Bayesian bootstrap versus classical bootstrap." Insurance: Mathematics and Economics 47, no. 1 (August 2010): 36–51. http://dx.doi.org/10.1016/j.insmatheco.2010.03.007.

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18

Schiegl, M. "On the Safety Loading for Chain Ladder Estimates: a Monte Carlo Simulation Study." ASTIN Bulletin 32, no. 1 (May 2002): 107–28. http://dx.doi.org/10.2143/ast.32.1.1018.

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AbstractA method for analysing the risk of taking a too low reserve level by the use of Chain Ladder method is developed. We give an answer to the question of how much safety loading in terms of the Chain Ladder standard error has to be added to the Chain Ladder reserve in order to reach a specified security level in loss reserving. This is an important question in the framework of integrated risk management of an insurance company. Furthermore we investigate the relative bias of Chain Ladder estimators. We use Monte Carlo simulation technique as well as the collective model of risk theory in each cell of run-off table. We analyse deviation between Chain Ladder reserves and Monte Carlo simulated reserves statistically. Our results document dependency on claim number and claim size distribution types and parameters.
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19

Riegel, Ulrich. "A QUANTITATIVE STUDY OF CHAIN LADDER BASED PRICING APPROACHES FOR LONG-TAIL QUOTA SHARES." ASTIN Bulletin 45, no. 2 (March 24, 2015): 267–307. http://dx.doi.org/10.1017/asb.2015.2.

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AbstractPricing approaches for long-tail quota shares are often based on the chain ladder method. Apart from IBNR calculation, common pricing methods require volume measures for accident years in the observation period, and for the quotation period. In practice, in most cases restated premiums are used as the volume measures. The prediction error of the chain ladder method is an important part of the prediction uncertainty of these pricing approaches. There are, however, two sources of uncertainty that are not addressed by the chain ladder model: the stochastic volatility of the claims in the first development year; and the restatement uncertainty, the risk that the restated premium is not a good volume measure. We extend Mack's chain ladder model to cover these two sources of uncertainty, and calculate the mean-squared error of chain ladder pricing approaches with arbitrary weights for the accident years in the observation period. Then we focus on the problem of finding optimal weights for the accident years. First, we assume that the parameters for restatement uncertainty are given, and provide recursion formulas to calculate approximately-optimal weights. Second, we describe a maximum likelihood approach that can be used to estimate the restatement uncertainty.
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20

Hess, Klaus Th, and Klaus D. Schmidt. "A comparison of models for the chain–ladder method." Insurance: Mathematics and Economics 31, no. 3 (December 2002): 351–64. http://dx.doi.org/10.1016/s0167-6687(02)00160-9.

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21

Merz, Michael, and Mario V. Wüthrich. "Prediction Error of the Multivariate Chain Ladder Reserving Method." North American Actuarial Journal 12, no. 2 (April 2008): 175–97. http://dx.doi.org/10.1080/10920277.2008.10597509.

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22

Adam, F. F. "Claim Reserving Estimation by Using the Chain Ladder Method." KnE Social Sciences 3, no. 11 (August 8, 2018): 1192. http://dx.doi.org/10.18502/kss.v3i11.2840.

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23

Merz, Michael, and Mario V. Wüthrich. "A credibility approach to the munich chain-ladder method." Blätter der DGVFM 27, no. 4 (October 2006): 619–28. http://dx.doi.org/10.1007/bf02809220.

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24

Mack, Thomas. "Which stochastic model is underlying the chain ladder method?" Insurance: Mathematics and Economics 15, no. 2-3 (December 1994): 133–38. http://dx.doi.org/10.1016/0167-6687(94)90789-7.

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25

Renshaw, A. E., and R. J. Verrall. "A Stochastic Model Underlying the Chain-Ladder Technique." British Actuarial Journal 4, no. 4 (October 1, 1998): 903–23. http://dx.doi.org/10.1017/s1357321700000222.

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ABSTRACTThis paper presents a statistical model underlying the chain-ladder technique. This is related to other statistical approaches to the chain-ladder technique which have been presented previously. The statistical model is cast in the form of a generalised linear model, and a quasi-likelihood approach is used. It is shown that this enables the method to process negative incremental claims. It is suggested that the chain-ladder technique represents a very narrow view of the possible range of models.
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26

Merz, M., and M. V. Wüthrich. "Prediction Error of the Chain Ladder Reserving Method applied to Correlated Run-off Triangles." Annals of Actuarial Science 2, no. 1 (March 2007): 25–50. http://dx.doi.org/10.1017/s1748499500000245.

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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.
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27

Wüthrich, Mario V., Michael Merz, and Hans Bühlmann. "Bounds on the estimation error in the chain ladder method." Scandinavian Actuarial Journal 2008, no. 4 (December 2008): 283–300. http://dx.doi.org/10.1080/03461230701723032.

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28

Verrall, R. J., and Z. Li. "Negative incremental claims: chain ladder and linear models." Journal of the Institute of Actuaries 120, no. 1 (1993): 171–83. http://dx.doi.org/10.1017/s0020268100036891.

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AbstractThis paper considers the application of loglinear models to claims run-off triangles which contain negative incremental claims. Maximum likelihood estimation is applied using the three parameter lognormal distribution. The method can be used in conjunction with any model which can be expressed in lognormal form. In particular the chain ladder technique is considered. An example is given and the results compared with the basic actuarial method.
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29

Buchwalder, Markus, Hans Bühlmann, Michael Merz, and Mario V. Wüthrich. "The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)." ASTIN Bulletin 36, no. 02 (November 2006): 521–42. http://dx.doi.org/10.2143/ast.36.2.2017933.

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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.
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30

Buchwalder, Markus, Hans Bühlmann, Michael Merz, and Mario V. Wüthrich. "The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited)." ASTIN Bulletin 36, no. 2 (November 2006): 521–42. http://dx.doi.org/10.1017/s0515036100014628.

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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.
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31

Verrall, R. J. "A Method for Modelling Varying Run-Off Evolutions in Claims Reserving." ASTIN Bulletin 24, no. 2 (November 1994): 325–32. http://dx.doi.org/10.2143/ast.24.2.2005074.

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AbstractThis paper considers the application of state space modelling to the chain ladder linear model in order to allow the run-off parameters to vary with accident year. In the usual application of the chain ladder technique, the development factors are assumed to be the same for each accident year. This implies that the run-off shape does not alter with accident year. This paper shows how this assumption can be relaxed in order to allow a recursive smooth model to be applied, or for large changes in the shape of the run-off curve. It is possible for these changes to be modelled using external inputs, or for a multiprocess model to be used to detect changes in the run-off shape.
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32

Wüthrich, Mario V. "Accounting Year Effects Modeling in the Stochastic Chain Ladder Reserving Method." North American Actuarial Journal 14, no. 2 (April 2010): 235–55. http://dx.doi.org/10.1080/10920277.2010.10597587.

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33

Kwon, Hyuk Sung, and Uy Quoc Vu. "Consideration of a structural-change point in the chain-ladder method." Communications for Statistical Applications and Methods 24, no. 3 (May 31, 2017): 211–26. http://dx.doi.org/10.5351/csam.2017.24.3.211.

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34

Wüthrich, Mario V., Michael Merz, and Natalia Lysenko. "Uncertainty of the claims development result in the chain ladder method." Scandinavian Actuarial Journal 2009, no. 1 (March 2009): 63–84. http://dx.doi.org/10.1080/03461230801979732.

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35

Schiegl, Magda. "A model study about the applicability of the Chain Ladder method." Scandinavian Actuarial Journal 2015, no. 6 (December 2, 2013): 482–99. http://dx.doi.org/10.1080/03461238.2013.852992.

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36

Verdonck, T., and M. Van Wouwe. "Detection and correction of outliers in the bivariate chain–ladder method." Insurance: Mathematics and Economics 49, no. 2 (September 2011): 188–93. http://dx.doi.org/10.1016/j.insmatheco.2011.04.003.

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37

Huergo, Luis, Jochen Heberle, and Michael Merz. "Bootstrapping the chain-ladder method for several correlated run-off portfolios." Zeitschrift für die gesamte Versicherungswissenschaft 98, no. 5 (January 16, 2010): 541–64. http://dx.doi.org/10.1007/s12297-009-0078-2.

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38

Elpidorou, Valandis, Carolin Margraf, María Dolores Martínez-Miranda, and Bent Nielsen. "A Likelihood Approach to Bornhuetter–Ferguson Analysis." Risks 7, no. 4 (December 10, 2019): 119. http://dx.doi.org/10.3390/risks7040119.

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A new Bornhuetter–Ferguson method is suggested herein. This is a variant of the traditional chain ladder method. The actuary can adjust the relative ultimates using externally estimated relative ultimates. These correspond to linear constraints on the Poisson likelihood underpinning the chain ladder method. Adjusted cash flow estimates were obtained as constrained maximum likelihood estimates. The statistical derivation of the new method is provided in the generalised linear model framework. A related approach in the literature, combining unconstrained and constrained maximum likelihood estimates, is presented in the same framework and compared theoretically. A data illustration is described using a motor portfolio from a Greek insurer.
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39

Braun, Christian. "The Prediction Error of the Chain Ladder Method Applied to Correlated Run-off Triangles." ASTIN Bulletin 34, no. 02 (November 2004): 399–423. http://dx.doi.org/10.2143/ast.34.2.505150.

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It is shown how the distribution-free method of Mack (1993) can be extended in order to estimate the prediction error of the Chain Ladder method for a portfolio of several correlated run-off triangles.
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40

Braun, Christian. "The Prediction Error of the Chain Ladder Method Applied to Correlated Run-off Triangles." ASTIN Bulletin 34, no. 2 (November 2004): 399–423. http://dx.doi.org/10.1017/s0515036100013751.

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It is shown how the distribution-free method of Mack (1993) can be extended in order to estimate the prediction error of the Chain Ladder method for a portfolio of several correlated run-off triangles.
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41

Triana, S., M. Novita, and S. F. Sari. "The Benktander claim reserving method, combining chain ladder method and Bornhuetter-Ferguson method using optimal credibility." Journal of Physics: Conference Series 1725 (January 2021): 012087. http://dx.doi.org/10.1088/1742-6596/1725/1/012087.

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42

Suwandani, Ria Novita, and Yogo Purwono. "Implementation of Gaussian Process Regression in Estimating Motor Vehicle Insurance Claims Reserves." Journal of Asian Multicultural Research for Economy and Management Study 2, no. 1 (February 11, 2021): 38–48. http://dx.doi.org/10.47616/jamrems.v2i1.77.

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This study aims to calculate the allowance for losses by applying Gaussian Process regression to estimate future claims. Modeling is done on motor vehicle insurance data. The data used in this study are historical data on PT XYZ's motor vehicle insurance business line during 2017 and 2019 (January 2017 to December 2019). Data analysis will be carried out on the 2017 - 2019 data to obtain an estimate of the claim reserves in the following year, namely 2018 - 2020. This study uses the Chain Ladder method which is the most popular loss reserving method in theory and practice. The estimation results show that the Gaussian Process Regression method is very flexible and can be applied without much adjustment. These results were also compared with the Chain Ladder method. Estimated claim reserves for PT XYZ's motor vehicle business line using the chain-ladder method, the company must provide funds for 2017 of 8,997,979,222 IDR in 2018 16,194,503,605 IDR in 2019 amounting to Rp. 1,719,764,520 for backup. Meanwhile, by using the Bayessian Gaussian Process method, the company must provide funds for 2017 of 9,060,965,077 IDR in 2018 amounting to 16,307,865,130 IDR, and in 2019 1,731,802,871 IDR for backup. The more conservative Bayessian Gaussian Process method. Motor vehicle insurance data has a short development time (claims occur) so that it is included in the short-tail type of business.
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43

Gisler, Alois. "The Estimation Error in the Chain-Ladder Reserving Method: A Bayesian Approach." ASTIN Bulletin 36, no. 02 (November 2006): 554–65. http://dx.doi.org/10.2143/ast.36.2.2017939.

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44

Gisler, Alois. "The Estimation Error in the Chain-Ladder Reserving Method: A Bayesian Approach." ASTIN Bulletin 36, no. 2 (November 2006): 554–65. http://dx.doi.org/10.1017/s0515036100014653.

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45

Karmila, S., S. Nurrohmah, and S. F. Sari. "Claim reserve prediction using the credibility theory for the Chain Ladder method." Journal of Physics: Conference Series 1442 (January 2020): 012038. http://dx.doi.org/10.1088/1742-6596/1442/1/012038.

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46

Shen, Han Xin, Wen Zhang Zhu, and Ai Yu Li. "Structure of Chromium Atomic Chains." Advanced Materials Research 415-417 (December 2011): 553–56. http://dx.doi.org/10.4028/www.scientific.net/amr.415-417.553.

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The geometric and electronic structures of Cr chains are studied by the first-principles of density-functional method. The present calculation results show that chromium can form planar chains in linear, zigzag, dimer, and ladder form one-dimensional structures. The most stable geometry chain among the studied structures is the ladder-form chain with five nearest neighbors. The dimer structure is found to be more stable than the zigzag one. Further more, the relative structural stability, the electronic energy bands, the density of states is discussed based on the ab initio calculations.
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47

Kocovic, Jelena, Mirela Mitrasevic, and Dejan Trifunovic. "Advantages and disadvantages of loss reserving methods in non-life insurance." Yugoslav Journal of Operations Research 29, no. 4 (2019): 553–61. http://dx.doi.org/10.2298/yjor180215003k.

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We analyse characteristics of the three most commonly used methods for estimating loss reserves in non life insurance: the chain ladder method, the loss ratio method, and the Bornhuetter-Ferguson method. Our aim is to give a comparative analysis of the results obtained from applying these methods to a practical case, and to put emphasis on their advantages and disadvantages.
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48

Mack, Thomas. "Credible Claims Reserves: the Benktander Method." ASTIN Bulletin 30, no. 2 (November 2000): 333–47. http://dx.doi.org/10.2143/ast.30.2.504639.

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AbstractA claims reserving method is reviewed which was introduced by Gunnar Benktander in 1976. It is a very intuitive credibility mixture of Bornhuetter/Ferguson and Chain Ladder. In this paper, the mean squared errors of all 3 methods are calculated and compared on the basis of a very simple stochastic model. The Benktander method is found to have almost always a smaller mean squared error than the other two methods and to be almost as precise as an exact Bayesian procedure.
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49

Zohry, Afaf Antar, and Mostafa Abdelghany Ahmed. "The Prediction Error of the Chain Ladder Method (With Application to Real Data)." International Journal of Economics and Finance 12, no. 12 (November 5, 2020): 14. http://dx.doi.org/10.5539/ijef.v12n12p14.

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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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50

Kremer, Erhard. "The correlated chain-ladder method for reserving in case of correlated claims developments." Blätter der DGVFM 27, no. 2 (October 2005): 315–22. http://dx.doi.org/10.1007/bf02808313.

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