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Journal articles on the topic 'Claims reserving'

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Published: 4 June 2021

Last updated: 30 January 2023

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1

Hesselager, Ole. "A Markov Model for Loss Reserving." ASTIN Bulletin 24, no. 2 (November 1994): 183–93. http://dx.doi.org/10.2143/ast.24.2.2005064.

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AbstractThe claims generating process for a non-life insurance portfolio is modelled as a marked Poisson process, where the mark associated with an incurred claim describes the development of that claim until final settlement. An unsettled claim is at any point in time assigned to a state in some state-space, and the transitions between different states are assumed to be governed by a Markovian law. All claims payments are assumed to occur at the time of transition between states. We develop separate expressions for the IBNR and RBNS reserves, and the corresponding prediction errors.

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2

Jessen, Anders Hedegaard, and Niels Rietdorf. "Diagonal effects in claims reserving." Scandinavian Actuarial Journal 2011, no. 1 (March 2011): 21–37. http://dx.doi.org/10.1080/03461230903301876.

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3

Renshaw, A. "Claims reserving by joint modelling." Insurance: Mathematics and Economics 17, no. 3 (April 1996): 239–40. http://dx.doi.org/10.1016/0167-6687(96)82389-4.

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4

Dupin, Gilles, Emmanuel Koenig, Pierre Le Moine, Alain Monfort, and Eric Ratiarison. "COHERENT INCURRED PAID (CIP) MODELS FOR CLAIMS RESERVING." ASTIN Bulletin 48, no. 02 (December 18, 2017): 749–77. http://dx.doi.org/10.1017/asb.2017.36.

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AbstractIn this paper, we first propose a statistical model, called the Coherent Incurred Paid model, to predict future claims, using simultaneously the information contained in incurred and paid claims. This model does not assume log-normality of the levels (or normality of the growth rates) and is semi-parametric since it only specifies the first and the second moments; however, in order to evaluate the impact of the normality assumption, we also propose a benchmark Gaussian version of our model. Correlations between growth rates of incurred and paid claims are allowed and the tail development period is estimated. We also provide methods for computing the Claim Development Results and their Values at Risk in the semi-parametric framework. Moreover, we show how to take into account the updating of the estimation in the computation of the Claim Development Results. An application highlights the practical importance of relaxing the normality assumption and of updating the estimation of the parameters.

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5

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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6

Mack, Thomas. "A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves." ASTIN Bulletin 21, no. 1 (April 1991): 93–109. http://dx.doi.org/10.2143/ast.21.1.2005403.

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AbstractIt is shown that there is a connection between rating in automobile insurance and the estimation of IBNR claims amounts because automobile insurance tariffs are mostly cross-classified by at least two variables (e.g. territory and driver class) and IBNR claims run-off triangles are always cross-classified by the two variables accident year and development year. Therefore, by translating the most well-known automobile rating methods into the claims reserving situation, some known and some unknown claims reserving methods are obtained. For instance, the automobile rating method of Bailey and Simon produces a new claims reserving method, whereas the model leading to the rating method called “marginal totals” produces the well-known IBNR claims estimation method called “chain ladder”. A drawback of this model is the fact that it is designed for the number of claims and not for the total claims amount for which it is usually applied.As an alternative for both, rating and claims reserving, we describe a simple but realistic parametric model for the total claims amount which is based on the Gamma distribution and has the advantage of providing the possibility of assessing the goodness-of-fit and calculating the estimation error. This method is not very well known in automobile insurance—although a satisfactory application is reported—and seems to be completely unknown in the field of claims reserving, although its execution is nearly as simple as that of the chain ladder method.

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7

Lemaire, Jean, and G. C. Taylor. "Claims Reserving in Non-Life Insurance." Journal of Risk and Insurance 55, no. 2 (June 1988): 396. http://dx.doi.org/10.2307/253338.

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8

Wüthrich, Mario V. "Machine learning in individual claims reserving." Scandinavian Actuarial Journal 2018, no. 6 (January 24, 2018): 465–80. http://dx.doi.org/10.1080/03461238.2018.1428681.

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9

England, P. D., and R. J. Verrall. "Stochastic Claims Reserving in General Insurance." British Actuarial Journal 8, no. 3 (August 1, 2002): 443–518. http://dx.doi.org/10.1017/s1357321700003809.

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ABSTRACTThis paper considers a wide range of stochastic reserving models for use in general insurance, beginning with stochastic models which reproduce the traditional chain-ladder reserve estimates. The models are extended to consider parametric curves and smoothing models for the shape of the development run-off, which allow extrapolation for the estimation of tail factors. The Bornhuetter-Ferguson technique is also considered, within a Bayesian framework, which allows expert opinion to be used to provide prior estimates of ultimate claims. The primary advantage of stochastic reserving models is the availability of measures of precision of reserve estimates, and in this respect, attention is focused on the root mean squared error of prediction (prediction error). Of greater interest is a full predictive distribution of possible reserve outcomes, and different methods of obtaining that distribution are described. The techniques are illustrated with examples throughout, and the wider issues discussed, in particular, the concept of a ‘best estimate’; reporting the variability of claims reserves; and use in dynamic financial analysis models.

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10

Verrall, Richard. "Claims reserving and generalised additive models." Insurance: Mathematics and Economics 19, no. 1 (December 1996): 31–43. http://dx.doi.org/10.1016/s0167-6687(96)00000-5.

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11

de Alba, Enrique, and Luis E. Nieto-Barajas. "Claims reserving: A correlated Bayesian model." Insurance: Mathematics and Economics 43, no. 3 (December 2008): 368–76. http://dx.doi.org/10.1016/j.insmatheco.2008.05.007.

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12

Merz, Michael, and Mario V. Wüthrich. "Paid–incurred chain claims reserving method." Insurance: Mathematics and Economics 46, no. 3 (June 2010): 568–79. http://dx.doi.org/10.1016/j.insmatheco.2010.02.004.

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13

Carroll, Patrick, and G. C. Taylor. "Claims Reserving in Non-Life Insurance." Journal of the Royal Statistical Society. Series A (General) 150, no. 2 (1987): 175. http://dx.doi.org/10.2307/2981647.

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14

Verrall, R. "Claims reserving and generalized additive models." Insurance: Mathematics and Economics 17, no. 3 (April 1996): 239. http://dx.doi.org/10.1016/0167-6687(96)82388-2.

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15

Zaçaj, Oriana, Endri Raço, Kleida Haxhi, Etleva Llagami, and Kostaq Hila. "Bootstrap Methods for Claims Reserving: R Language Approach." WSEAS TRANSACTIONS ON MATHEMATICS 21 (May 20, 2022): 252–59. http://dx.doi.org/10.37394/23206.2022.21.30.

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Bootstrap methods have been used by actuaries for a long time to predict future claims cash flows and their variability. This work aims to illustrate the use of bootstrap methods in practice, taking as an example the claims development data of the personal accident portfolio from the largest insurance company in Albania, over a period of 10 years. It is not the objective of this work to provide a theoretical analysis of the bootstrap methods, rather, this work focuses on highlighting the benefits of using bootstrap methods to predict the distribution of future claims development, and estimate the standard error, for a better risk assessment of liabilities within insurance companies. This work is divided into two well-differentiated phases: the first is to select the theoretical probability distribution that best fits the available claims dataset. Comparison of distributions is facilitated by the possibilities offered by the R programming languages. Both, the maximum likelihood parameter estimation method and the chi-square goddess goodness of fit test, are used to specify the probability distribution that best fits the data, among a family of predefined distributions. The results show that the Gamma distribution better describes the claim development data. The next phase is to use bootstrap methods, based on the selected distribution, to estimate the ultimate value of claims, the claims reserve, and their standard error.

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16

Lopez, Olivier, Xavier Milhaud, and Pierre-E. Thérond. "A TREE-BASED ALGORITHM ADAPTED TO MICROLEVEL RESERVING AND LONG DEVELOPMENT CLAIMS." ASTIN Bulletin 49, no. 03 (May 7, 2019): 741–62. http://dx.doi.org/10.1017/asb.2019.12.

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AbstractIn non-life insurance, business sustainability requires accurate and robust predictions of reserves related to unpaid claims. To this aim, two different approaches have historically been developed: aggregated loss triangles and individual claim reserving. The former has reached operational great success in the past decades, whereas the use of the latter still remains limited. Through two illustrative examples and introducing an appropriate tree-based algorithm, we show that individual claim reserving can be really promising, especially in the context of long-term risks.

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17

Parodi, Pietro. "Triangle-free reserving." British Actuarial Journal 19, no. 1 (May 13, 2013): 168–218. http://dx.doi.org/10.1017/s1357321713000093.

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AbstractThis paper argues that all reserving methods based on claims triangulations (the “triangle trick”), no matter how sophisticated the subsequent processing of the information contained in the triangle is, are inherently inadequate to accurately model the distribution of reserves, although they may be good enough to produce a point estimate of such reserves. The reason is that the triangle representation involves the compression (and ultimately the loss) of crucial information about the individual losses, which comes back to haunt us when we try to extract detailed information on the distribution of incurred but not reported (IBNR) and reported but not settled (RBNS) losses.This paper then argues that in order to avoid such loss of information it is necessary to adopt an approach which is similar to that used in pricing, where a separate frequency and severity model are developed and then combined by Monte Carlo simulation or other numerical techniques to produce the aggregate loss distribution.A specific implementation of this approach is described, whose core feature is a method to produce a frequency model for the incurred but not reported claim count based on the empirical distribution of delays (delay = the time between loss date and reporting date), after adjustments to make up for the bias towards smaller delays. The method also produces a kernel severity model for the individual losses, from which the severity distribution of each year of occurrence can be derived. By combining the frequency and severity model in the usual way (e.g. through Monte Carlo simulation), an aggregate model for IBNR and UPR losses can be produced.As for RBNS losses, we suggest using one of the many methods to analyse the distribution of IBNER (incurred but not enough reserved) factors to produce a possible distribution of outcomes.A case study based on real-world liability claims is used to illustrate how the method works in practice.Also, in a first step towards validating the method for calculating IBNR and comparing it with existing methods, a series of experiments with artificial data sets was undertaken, which show a drastic reduction in the prediction error of both the IBNR claim count and the IBNR total amount with respect to the standard chain ladder method. And what is perhaps most promising, the experiments show that the distribution of IBNR reserves is much closer (in terms of the Kolmogorov-Smirnov distance) to the “true” one than that based on Mack's method in the way it is normally applied. The method promises therefore a more accurate assessment of the uncertainty around reserves.

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18

Bischofberger, Stephan M. "In-Sample Hazard Forecasting Based on Survival Models with Operational Time." Risks 8, no. 1 (January 3, 2020): 3. http://dx.doi.org/10.3390/risks8010003.

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We introduce a generalization of the one-dimensional accelerated failure time model allowing the covariate effect to be any positive function of the covariate. This function and the baseline hazard rate are estimated nonparametrically via an iterative algorithm. In an application in non-life reserving, the survival time models the settlement delay of a claim and the covariate effect is often called operational time. The accident date of a claim serves as covariate. The estimated hazard rate is a nonparametric continuous-time alternative to chain-ladder development factors in reserving and is used to forecast outstanding liabilities. Hence, we provide an extension of the chain-ladder framework for claim numbers without the assumption of independence between settlement delay and accident date. Our proposed algorithm is an unsupervised learning approach to reserving that detects operational time in the data and adjusts for it in the estimation process. Advantages of the new estimation method are illustrated in a data set consisting of paid claims from a motor insurance business line on which we forecast the number of outstanding claims.

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19

Wright, T. S. "A stochastic method for claims reserving in general insurance." Journal of the Institute of Actuaries 117, no. 3 (December 1990): 677–731. http://dx.doi.org/10.1017/s0020268100043262.

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AbstractThe paper addresses the problem of estimating future claim payments from the ‘run-off’ of past claim payments. A model of the claim payment process is postulated. Results from risk theory are applied to give a model for the incremental paid claims data by development period. A fitting method is developed which takes account of the error structure of the data implied by the underlying model of the claim payment process. The application of a similar method to incremental incurred data is considered. A numerical example is given.

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20

Felice, Massimo De, and Franco Moriconi. "Claim Watching and Individual Claims Reserving Using Classification and Regression Trees." Risks 7, no. 4 (October 12, 2019): 102. http://dx.doi.org/10.3390/risks7040102.

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We present an approach to individual claims reserving and claim watching in general insurance based on classification and regression trees (CART). We propose a compound model consisting of a frequency section, for the prediction of events concerning reported claims, and a severity section, for the prediction of paid and reserved amounts. The formal structure of the model is based on a set of probabilistic assumptions which allow the provision of sound statistical meaning to the results provided by the CART algorithms. The multiperiod predictions required for claims reserving estimations are obtained by compounding one-period predictions through a simulation procedure. The resulting dynamic model allows the joint modeling of the case reserves, which usually yields useful predictive information. The model also allows predictions under a double-claim regime, i.e., when two different types of compensation can be required by the same claim. Several explicit numerical examples are provided using motor insurance data. For a large claims portfolio we derive an aggregate reserve estimate obtained as the sum of individual reserve estimates and we compare the result with the classical chain-ladder estimate. Backtesting exercises are also proposed concerning event predictions and claim-reserve estimates.

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21

Gabrielli, Andrea. "A NEURAL NETWORK BOOSTED DOUBLE OVERDISPERSED POISSON CLAIMS RESERVING MODEL." ASTIN Bulletin 50, no. 1 (December 17, 2019): 25–60. http://dx.doi.org/10.1017/asb.2019.33.

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AbstractWe present an actuarial claims reserving technique that takes into account both claim counts and claim amounts. Separate (overdispersed) Poisson models for the claim counts and the claim amounts are combined by a joint embedding into a neural network architecture. As starting point of the neural network calibration, we use exactly these two separate (overdispersed) Poisson models. Such a nested model can be interpreted as a boosting machine. It allows us for joint modeling and mutual learning of claim counts and claim amounts beyond the two individual (overdispersed) Poisson models.

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22

Haastrup, Svend, and Elja Arjas. "Claims Reserving in Continuous Time; A Nonparametric Bayesian Approach." ASTIN Bulletin 26, no. 2 (November 1996): 139–64. http://dx.doi.org/10.2143/ast.26.2.563216.

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AbstractOccurrences and developments of claims are modelled as a marked point process. The individual claim consists of an occurrence time, two covariates, a reporting delay, and a process describing partial payments and settlement of the claim. Under certain likelihood assumptions the distribution of the process is described by 14 one-dimensional components. The modelling is nonparametric Bayesian. The posterior distribution of the components and the posterior distribution of the outstanding IBNR and RBNS liabilities are found simultaneously. The method is applied to a portfolio of accident insurances.

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23

Chukhrova, Nataliya, and Arne Johannssen. "Stochastic Claims Reserving Methods with State Space Representations: A Review." Risks 9, no. 11 (November 4, 2021): 198. http://dx.doi.org/10.3390/risks9110198.

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Often, the claims reserves exceed the available equity of non-life insurance companies and a change in the claims reserves by a small percentage has a large impact on the annual accounts. Therefore, it is of vital importance for any non-life insurer to handle claims reserving appropriately. Although claims data are time series data, the majority of the proposed (stochastic) claims reserving methods is not based on time series models. Among the time series models, state space models combined with Kalman filter learning algorithms have proven to be very advantageous as they provide high flexibility in modeling and an accurate detection of the temporal dynamics of a system. Against this backdrop, this paper aims to provide a comprehensive review of stochastic claims reserving methods that have been developed and analyzed in the context of state space representations. For this purpose, relevant articles are collected and categorized, and the contents are explained in detail and subjected to a conceptual comparison.

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24

Rolski, T., and A. Tomanek. "A continuous-time model for claims reserving." Applicationes Mathematicae 41, no. 4 (2014): 277–300. http://dx.doi.org/10.4064/am41-4-1.

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25

Wüthrich, Mario V. "Claims Reserving Using Tweedie's Compound Poisson Model." ASTIN Bulletin 33, no. 02 (November 2003): 331–46. http://dx.doi.org/10.2143/ast.33.2.503696.

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We consider the problem of claims reserving and estimating run-off triangles. We generalize the gamma cell distributions model which leads to Tweedie's compound Poisson model. Choosing a suitable parametrization, we estimate the parameters of our model within the framework of generalized linear models (see Jørgensen-de Souza [2] and Smyth-Jørgensen [8]). We show that these methods lead to reasonable estimates of the outstanding loss liabilities.

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26

Noviyanti, Lienda, R. Hasna Afifah, A. Zanbar Soleh, and Anna Chadidjah. "Estimation Claims Reserving Based on Archimedean Copula." Journal of Physics: Conference Series 1306 (August 2019): 012013. http://dx.doi.org/10.1088/1742-6596/1306/1/012013.

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27

Bühlmann, Hans, and Franco Moriconi. "CREDIBILITY CLAIMS RESERVING WITH STOCHASTIC DIAGONAL EFFECTS." ASTIN Bulletin 45, no. 2 (April 27, 2015): 309–53. http://dx.doi.org/10.1017/asb.2015.3.

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AbstractAn interesting class of stochastic claims reserving methods is given by the models with conditionally independent loss increments (CILI), where the incremental losses are conditionally independent given a risk parameter Θi,j depending on both the accident year i and the development year j. The Bühlmann–Straub credibility reserving (BSCR) model is a particular case of a CILI model where the risk parameter is only depending on i. We consider CILI models with additive diagonal risk (ADR), where the risk parameter is given by the sum of two components, one depending on the accident year i and the other depending on the calendar year t = i + j. The model can be viewed as an extension of the BSCR model including random diagonal effects, which are often declared to be important in loss reserving but rarely are specifically modeled. We show that the ADR model is tractable in closed form, providing credibility formulae for the reserve and the mean square error of prediction (MSEP). We also derive unbiased estimators for the variance parameters which extend the classical Bühlmann–Straub estimators. The results are illustrated by a numerical example and the estimators are tested by simulation. We find that the inclusion of random diagonal effects can be significant for the reserve estimates and, especially, for the evaluation of the MSEP. The paper is written with the purpose of illustrating the role of stochastic diagonal effects. To isolate these effects, we assume that the development pattern is given. In particular, our MSEP values do not include the uncertainty due to the estimation of the development pattern.

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Portugal, Luís, Athanasios A. Pantelous, and Hirbod Assa. "Claims Reserving with a Stochastic Vector Projection." North American Actuarial Journal 22, no. 1 (November 9, 2017): 22–39. http://dx.doi.org/10.1080/10920277.2017.1353429.

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29

Wüthrich, Mario V. "Claims Reserving Using Tweedie's Compound Poisson Model." ASTIN Bulletin 33, no. 2 (November 2003): 331–46. http://dx.doi.org/10.1017/s0515036100013490.

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We consider the problem of claims reserving and estimating run-off triangles. We generalize the gamma cell distributions model which leads to Tweedie's compound Poisson model. Choosing a suitable parametrization, we estimate the parameters of our model within the framework of generalized linear models (see Jørgensen-de Souza [2] and Smyth-Jørgensen [8]). We show that these methods lead to reasonable estimates of the outstanding loss liabilities.

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30

Hudecová, Šárka, and Michal Pešta. "Modeling dependencies in claims reserving with GEE." Insurance: Mathematics and Economics 53, no. 3 (November 2013): 786–94. http://dx.doi.org/10.1016/j.insmatheco.2013.09.018.

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31

Peters, Gareth W., Rodrigo S. Targino, and Mario V. Wüthrich. "Full Bayesian analysis of claims reserving uncertainty." Insurance: Mathematics and Economics 73 (March 2017): 41–53. http://dx.doi.org/10.1016/j.insmatheco.2016.12.007.

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32

Okine, A. Nii-Armah, Edward W. Frees, and Peng Shi. "JOINT MODEL PREDICTION AND APPLICATION TO INDIVIDUAL-LEVEL LOSS RESERVING." ASTIN Bulletin 52, no. 1 (November 5, 2021): 91–116. http://dx.doi.org/10.1017/asb.2021.28.

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AbstractInnon-life insurance, the payment history can be predictive of the timing of a settlement for individual claims. Ignoring the association between the payment process and the settlement process could bias the prediction of outstanding payments. To address this issue, we introduce into the literature of micro-level loss reserving a joint modeling framework that incorporates longitudinal payments of a claim into the intensity process of claim settlement. We discuss statistical inference and focus on the prediction aspects of the model. We demonstrate applications of the proposed model in the reserving practice with a detailed empirical analysis using data from a property insurance provider. The prediction results from an out-of-sample validation show that the joint model framework outperforms existing reserving models that ignore the payment–settlement association.

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33

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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Meng, Shengwang, and Guangyuan Gao. "COMPOUND POISSON CLAIMS RESERVING MODELS: EXTENSIONS AND INFERENCE." ASTIN Bulletin 48, no. 3 (May 11, 2018): 1137–56. http://dx.doi.org/10.1017/asb.2018.12.

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AbstractWe consider compound Poisson claims reserving models applied to the paid claims and to the number of payments run-off triangles. We extend the standard Poisson-gamma assumption to account for over-dispersion in the payment counts and to account for various mean and variance structures in the individual payments. Two generalized linear models are applied consecutively to predict the unpaid claims. A bootstrap is used to estimate the mean squared error of prediction and to simulate the predictive distribution of the unpaid claims. We show that the extended compound Poisson models make reasonable predictions of the unpaid claims.

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35

Alai, D. H., M. Merz, and M. V. Wüthrich. "Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method." Annals of Actuarial Science 4, no. 1 (March 2009): 7–31. http://dx.doi.org/10.1017/s1748499500000580.

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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.

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36

Gerthofer, Michal, and Michal Pešta. "Stochastic Claims Reserving in Insurance Using Random Effects." Prague Economic Papers 26, no. 5 (October 1, 2017): 542–60. http://dx.doi.org/10.18267/j.pep.625.

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37

Shim, Jooyong, and Changha Hwang. "Kernel Poisson regression machine for stochastic claims reserving." Journal of the Korean Statistical Society 40, no. 1 (March 2011): 1–9. http://dx.doi.org/10.1016/j.jkss.2010.01.004.

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38

Heberle, Jochen, and Anne Thomas. "Combining chain-ladder claims reserving with fuzzy numbers." Insurance: Mathematics and Economics 55 (March 2014): 96–104. http://dx.doi.org/10.1016/j.insmatheco.2014.01.002.

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39

Huerlimann, Werner. "A simple multi-state gamma claims reserving model." International Journal of Contemporary Mathematical Sciences 10 (2015): 65–77. http://dx.doi.org/10.12988/ijcms.2015.515.

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40

Pentikäinen, Teivo, and Jukka Rantala. "A Simulation Procedure for Comparing Different Claims Reserving Methods." ASTIN Bulletin 22, no. 2 (November 1992): 191–216. http://dx.doi.org/10.2143/ast.22.2.2005115.

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AbstractThe estimation of outstanding claims is one of the important aspects in the management of the insurance business. Various methods have been widely dealt with in the actuarial literature. Exploration of the inaccuracies involved is traditionally based on a post-facto comparison of the estimates against the actual outcomes of the settled claims. However, until recent years it has not been usual to consider the inaccuracies inherent in claims reserving in the context of more comprehensive (risk theoretical) models, the purpose of which is to analyse the insurer as a whole. Important parts of the technique which will be outlined in this paper can be incorporated into over-all risk theory models to introduce the uncertainty involved with technical reserves as one of the components in solvency and other analyses (Pentikäinen et al. (1989)).The idea in this paper is to describe a procedure by which one can explore how various reserving methods react to fictitious variations, fluctuations, trends, etc. which might influence the claims process, and, what is most important, how they reflect on the variables indicating the financial position of the insurer. For this purpose, a claims process is first postulated and claims are simulated and ordered to correspond to an actual handling of the observed claims of a fictitious insurer. Next, the simulation program will ‘mime’ an actuary who is calculating the claims reserve on the basis of these ‘observed’ claims data. Finally, the simulation is further continued thus generating the settlement of the reserved claims. The difference between reserved amounts and settled amounts gives the reserving (run-off) error in this particular simulated case. By repeating the simulation numerous times (Monte Carlo method) the distribution of the error can be estimated as well as its effect on the total outcome of the insurer.

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Happ, Sebastian, and Mario V. Wüthrich. "PAID-INCURRED CHAIN RESERVING METHOD WITH DEPENDENCE MODELING." ASTIN Bulletin 43, no. 1 (January 2013): 1–20. http://dx.doi.org/10.1017/asb.2012.4.

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AbstractThe paid-incurred chain (PIC) reserving method is a claims reserving method that allows to combine claims payments and incurred losses information in a mathematical consistent way. The main criticism on the original Bayesian log-normal PIC model presented in Merz–Wüthrich [5] is that it does not respect dependence properties within the observed data. In the present paper, we extend the original Bayesian log-normal PIC model so that dependence is modeled in an appropriate way.

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Craighead, D. H. "Reserving for catastrophe reinsurance." Journal of the Institute of Actuaries 121, no. 1 (1994): 135–60. http://dx.doi.org/10.1017/s0020268100020114.

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AbstractThe paper sets out the method required to be followed when estimating reserves for a Company or a Lloyd's Syndicate which has accepted reinsurance treaties that have given rise to catastrophe losses, sufficiently large to upset the normal development pattern and to affect the gross account quite differently from the net account. The losses may be caused by single factors such as aircraft crashes or oil rig disasters, or by the aggregation of claims resulting from a windstorm or an earthquake. The paper discusses two possible approaches to estimation of the gross losses; via exposure totals or via statistical modelling techniques.

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Lindholm, Mathias, and Henning Zakrisson. "A COLLECTIVE RESERVING MODEL WITH CLAIM OPENNESS." ASTIN Bulletin 52, no. 1 (December 3, 2021): 117–43. http://dx.doi.org/10.1017/asb.2021.33.

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AbstractThe present paper introduces a simple aggregated reserving model based on claim count and payment dynamics, which allows for claim closings and re-openings. The modelling starts off from individual Poisson process claim dynamics in discrete time, keeping track of accident year, reporting year and payment delay. This modelling approach is closely related to the one underpinning the so-called double chain-ladder model, and it allows for producing separate reported but not settled and incurred but not reported reserves. Even though the introduction of claim closings and re-openings will produce new types of dependencies, it is possible to use flexible parametrisations in terms of, for example, generalised linear models (GLM) whose parameters can be estimated based on aggregated data using quasi-likelihood theory. Moreover, it is possible to obtain interpretable and explicit moment calculations, as well as having consistency of normalised reserves when the number of contracts tend to infinity. Further, by having access to simple analytic expressions for moments, it is computationally cheap to bootstrap the mean squared error of prediction for reserves. The performance of the model is illustrated using a flexible GLM parametrisation evaluated on non-trivial simulated claims data. This numerical illustration indicates a clear improvement compared with models not taking claim closings and re-openings into account. The results are also seen to be of comparable quality with machine learning models for aggregated data not taking claim openness into account.

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Peters, Gareth W., Pavel V. Shevchenko, and Mario V. Wüthrich. "Model Uncertainty in Claims Reserving within Tweedie's Compound Poisson Models." ASTIN Bulletin 39, no. 1 (May 2009): 1–33. http://dx.doi.org/10.2143/ast.39.1.2038054.

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AbstractIn this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated into the prediction. We consider both the model selection problem and the model averaging solutions for the predicted reserves. As a part of this process we also consider the sub problem of variable selection to obtain a parsimonious representation of the model being fitted.

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Pigeon and Duval. "Individual Loss Reserving Using a Gradient Boosting-Based Approach." Risks 7, no. 3 (July 12, 2019): 79. http://dx.doi.org/10.3390/risks7030079.

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In this paper, we propose models for non-life loss reserving combining traditionalapproaches such as Mack’s or generalized linear models and gradient boosting algorithm in anindividual framework. These claim-level models use information about each of the payments madefor each of the claims in the portfolio, as well as characteristics of the insured. We provide an examplebased on a detailed dataset from a property and casualty insurance company. We contrast sometraditional aggregate techniques, at the portfolio-level, with our individual-level approach and wediscuss some points related to practical applications.

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Gigante, Patrizia, Liviana Picech, and Luciano Sigalotti. "CALENDAR YEAR EFFECT MODELING FOR CLAIMS RESERVING IN HGLM." ASTIN Bulletin 49, no. 03 (July 19, 2019): 763–86. http://dx.doi.org/10.1017/asb.2019.22.

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AbstractClaims reserving models are usually based on data recorded in run-off tables, according to the origin and the development years of the payments. The amounts on the same diagonal are paid in the same calendar year and are influenced by some common effects, for example, claims inflation, that can induce dependence among payments. We introduce hierarchical generalized linear models (HGLM) with risk parameters related to the origin and the calendar years, in order to model the dependence among payments of both the same origin year and the same calendar year. Besides the random effects, the linear predictor also includes fixed effects. All the parameters are estimated within the model by the h-likelihood approach. The prediction for the outstanding claims and an approximate formula to evaluate the mean square error of prediction are obtained. Moreover, a parametric bootstrap procedure is delineated to get an estimate of the predictive distribution of the outstanding claims. A Poisson-gamma HGLM with origin and calendar year effects is studied extensively and a numerical example is provided. We find that the estimates of the correlations can be significant for payments in the same calendar year and that the inclusion of calendar effects can determine a remarkable impact on the prediction uncertainty.

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Renshaw, A. E. "Chain ladder and interactive modelling. (Claims reserving and GLIM)." Journal of the Institute of Actuaries 116, no. 3 (December 1989): 559–87. http://dx.doi.org/10.1017/s0020268100036702.

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The prediction of outstanding claims amounts in non-life insurance is, by its very nature, highly speculative. Partially because of this and partially because of the variety of features suggested by various researchers for possible inclusion in the structure of the underlying prediction model, the past two decades have seen a proliferation of methodologies for making such predictions. Specific details of these developments are contained in a comprehensive and highly detailed survey conducted by Taylor (1986) in which a taxonomy of methods is established. One feature common to all of these methods is the utilization of current and past records of claims amounts—invariably in the form of the familiar so-called runoff triangle or a variant thereof—to calibrate the proposed prediction model before use. Prudence dictates that diagnostic checks should then be made to establish whether or not the data are supportive of the structure imparted to the prediction model before use, a feature which apart from some notable exceptions including Zehnwirth (1985) and Taylor (1983), is not always emphasized in the literature.

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Gigante, Patrizia, Liviana Picech, and Luciano Sigalotti. "Claims reserving in the hierarchical generalized linear model framework." Insurance: Mathematics and Economics 52, no. 2 (March 2013): 381–90. http://dx.doi.org/10.1016/j.insmatheco.2013.02.006.

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Djehiche, Boualem, and Björn Löfdahl. "Risk aggregation and stochastic claims reserving in disability insurance." Insurance: Mathematics and Economics 59 (November 2014): 100–108. http://dx.doi.org/10.1016/j.insmatheco.2014.09.001.

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Taylor, Greg, Gráinne McGuire, and James Sullivan. "Individual Claim Loss Reserving Conditioned by Case Estimates." Annals of Actuarial Science 3, no. 1-2 (September 2008): 215–56. http://dx.doi.org/10.1017/s1748499500000518.

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ABSTRACTThis paper examines various forms of individual claim model for the purpose of loss reserving, with emphasis on the prediction error associated with the reserve. Each form of model is calibrated against a single extensive data set, and then used to generate a forecast of loss reserve and an estimate of its prediction error.The basis of this is a model of the “paids” type, in which the sizes of strictly positive individual finalised claims are expressed in terms of a small number of covariates, most of which are in some way functions of time. Such models can be found in the literature.The purpose of the current paper is to extend these to individual claim “incurreds” models. These are constructed by the inclusion of case estimates in the model's conditioning information. This form of model is found to involve rather more complexity in its structure.For the particular data set considered here, this did not yield any direct improvement in prediction error. However, a blending of the paids and incurreds models did so.

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