Chain Ladder Research Articles

ESTIMATION OF CLAIM RESERVES USING THE CHAIN LADDER METHOD

One form and effort in dealing with all the risks that might occur in the future is insurance. In managing premiums paid by insurance participants, insurance companies must also consider unexpected claims that may occur in the future. Therefore, a method is needed that can be used by insurance companies to prepare claim reserves for the future. One method that is often used is the Chain Ladder method. This research aims to predict and estimate the claim reserves that insurance companies must prepare in the face of unexpected claims in the future. Based on the results of this study, the amount of claims that the company must prepare to deal with claims that may occur in 2020 is USD 1,110,879.00.

Risk Management of Insurance Companies With The Implementation Of The Munich Chain Ladder Method In Claim Reserve Estimation

Risk Management of Insurance Companies With The Implementation Of The Munich Chain Ladder Method In Claim Reserve Estimation

Estimating the effective reproduction number of COVID-19 via the chain ladder method

Estimating the effective reproduction number of COVID-19 via the chain ladder method

Claim Reserves Estimation Using Chain Ladder Method in Casualty Insurance for the Period 2010 - 2019

In a work environment, the presence of risk or unforeseeable events is inevitable, as employees certainly seek to get a sense of security in doing work. Therefore, insurance is responsibility to provide sense of security to employees by providing protection in the form of claim payments to employees who get accidents. To meet the claim payment, insurance companies need to prepare funds. With the chain ladder method, insurance companies can estimate how much funds must be prepared to make claim payments. This study used the secondary data from general insurance companies in the United States published by the National Association of Insurance Commissioners under the title "Statistical Compilation of Annual Statement Information for Property/Casualty Insurance Companies in 2019". Data in the form of cumulative run-off triangle with accident period 2010-2019. Through this calculation, claim reserves that must be prepared by insurance companies for 2020 amounted to USD 1,553,906.

Mack’s estimator motivated by large exposure asymptotics in a compound poisson setting

AbstractThe distribution-free chain ladder of Mack justified the use of the chain ladder predictor and enabled Mack to derive an estimator of conditional mean squared error of prediction for the chain ladder predictor. Classical insurance loss models, that is of compound Poisson type, are not consistent with Mack’s distribution-free chain ladder. However, for a sequence of compound Poisson loss models indexed by exposure (e.g., number of contracts), we show that the chain ladder predictor and Mack’s estimator of conditional mean squared error of prediction can be derived by considering large exposure asymptotics. Hence, quantifying chain ladder prediction uncertainty can be done with Mack’s estimator without relying on the validity of the model assumptions of the distribution-free chain ladder.

Bootstrap consistency for the Mack bootstrap

Mack's distribution-free chain ladder reserving model belongs to the most popular approaches in non-life insurance mathematics. Proposed to determine the first two moments of the reserve, it does not allow to identify the whole distribution of the reserve. For this purpose, Mack's model is usually equipped with a tailor-made bootstrap procedure. Although widely used in practice to estimate the reserve risk, no theoretical bootstrap consistency results exist that justify this approach.To fill this gap in the literature, we adopt the framework proposed by Steinmetz and Jentsch (2022) to derive asymptotic theory in Mack's model. By splitting the reserve into two parts corresponding to process and estimation uncertainty, this enables - for the first time - a rigorous investigation also of the validity of the Mack bootstrap. We prove that the (conditional) distribution of the asymptotically dominating process uncertainty part is correctly mimicked by Mack's bootstrap if the parametric family of distributions of the individual development factors is correctly specified. Otherwise, this is not the case. In contrast, the (conditional) distribution of the estimation uncertainty part is generally not correctly captured by Mack's bootstrap. To tackle this, we propose an alternative Mack-type bootstrap, which is designed to capture also the distribution of the estimation uncertainty part.We illustrate our findings by simulations and show that the newly proposed alternative Mack bootstrap performs superior to the Mack bootstrap.

Measurement Claim Reserving Insurance Contract in Accordance with IFRS 17 using Stochastic State Space Model

International Financial Reporting Standard 17 (IFRS 17) is a global accounting standard developed by the International Accounting Standards Board (IASB). It guides the accounting treatment of insurance contracts in financial statements. In IFRS 17, claim reserving is vital for measuring insurance contracts and determining the Contractual Service Margin (CSM). The claim reserving process involves estimating expected claim payouts over the contract’s duration. These estimates are crucial for calculating the liability for incurred claims and determining the CSM, representing unearned profit. Claim data is treated as ordered data by sorting the run-off triangle row-wise, resulting univariate time series with missing values. The state space model provides a framework for modeling time series, assuming system development over time. By taking the log of claim data so that the data is normally distributed, the lognormal state space model, along with Kalman recursion algorithms, can be applied for Incurred but Not Reported (IBNR) projections. The lognormal state space model’s IBNR reserve estimate is more precise and sufficient to compensate loss than the chain ladder method. Furthermore, the performance of the lognormal state space model outperforms the chain ladder method by means of model validation using RMSE, MAE, RSE, and R2.

The Comparison of Estimated Reserve Claims with the Classical Chain Ladder and Bornhuetter-Double Chain Ladder Method

In the world of insurance, insurance companies need to back up claims to ensure that the company can cover expenses resulting from filing claims from policyholders. Claim reserves represent the estimated value of claim payments in the future, where there are differences in the estimated and actual value of claim payments. Errors in predicting claim reserves will result in inaccuracies and disrupt the insurance company's financial stability. There are several ways to estimate claim reserves, one of the most common methods is using a Chain Ladder. However, the Chain Ladder method is very susceptible to outliers, so another method is needed to estimate claims reserves that are more accurate. This study discusses the comparison between the Chain Ladder method and one of the development methods, namely Bornhuetter-Double Chain Ladder in estimating claim reserves. The Bornhuetter-Double Chain Ladder method uses data on claims that have occurred as a whole, the amount of claims that have been paid, and the number of claims that have occurred. Based on the research results, it can be concluded that the Bornhuetter-Double Chain Ladder method is capable of producing more stable and accurate claim reserves compared to the Chain Ladder method.

An actuarial comparison of loss-ratio-Bornhuetter-Ferguson and classical chain ladder techniques in insurance loss reserving: A computational approach

An insurance firm promises to reimburse benefits to the insured when unforeseen events evolve. When such contingencies arise, the underwriter has a liability to pay the claim through loss reserving techniques. The estimation of such loss reserving should be technically performed so the insurance firm will not run into a loss. This study aims to (i) estimate the Bornheutter-Ferguson reserve and the inverse of its development factor λn under the aegis of the loss ratio framework. (ii) numerically estimate the chain ladder reserve and final losses, (iii) estimate the Ratio of cumulative payments in successive development periods, and (iv) demonstrate to professional insurance firms how to use these techniques in practice. These techniques evaluated through some run-off loss matrix can be employed to estimate technical provisions for the outstanding claims. Computational evidence from our results over the periods analyzed confirms that on the assumption of 0.9 the loss ratio, the Bornheutter- Ferguson technique as an actuarial extension of the chain ladder method numerically presents a lower reserve value than the corresponding chain ladder reserve, and hence CLreserve=249,811.708>BFreserve=86,612.58.

PENGGUNAAN METODE BORNHUETTER-FERGUSON UNTUK ESTIMASI CADANGAN KLAIM

Health insurance company have to determine claim reserve that’s suitable with the existing condition. There is three party that’s involved in the health insurance management, namely the policy holder, Admedika as the third party administration, and also the insurance company itself as the (insurer). When the policy holder obtained treatments whose financing is done through a health insurance, then the health insurance company have the obligation to finish the financial matters. Delays in payments from insurance companies to health facilities are caused, among others, by the administrative process. Thus, every claim submitted by the insured party to the insurance company will be settled in stages to the health facilities. The data presented from these conditions form a triangle matrix (run-off triangle) which then becomes the basis for estimating the amount of IBNR claims reserves. The Bornhuetter-Ferguson (BF) method involves the amount of premium that has become income for the company and calculates the Ultimate Claim value in estimating the amount of claim reserves. This method is the result of the development of the previous method, Chain-Ladder (CL), which only relies on historical data on claim payments. Premium calculations need to be involved in health insurance, because the insurance period is short, which is only one year. Insurance companies haven't had time to turn around the money to invest, so payment of claims will depend more on the premium that becomes income for the company (earned premium). The estimated claim reserve value is more suitable and robust than the CL method. Estimated claim reserves that occur in the 2nd event period amount to IDR50,658,714 with an estimated interval for the 2nd event period between IDR10,215,477 and IDR91,101,950

ANALYSIS OF ROBUST CHAIN LADDER METHOD IN ESTIMATING AUSTRALIAN MOTOR INSURANCE RESERVES WITH OUTLYING DATASET

Reserves are one of the most crucial components for an insurance company to make sure it has enough money to pay off all the incurred claims. The presence of outliers in the incurred claims data harbors risk on inaccurately predicting reserves to cover claim amounts, usually achieved by the standard chain ladder reserving method. To remedy the effect of the outliers, the robust chain ladder reserving method is used by setting the median value to predict estimated reserve. On this research, we utilized both methods on various datasets. The purpose of this paper is to determine the best method that can be utilized by insurance company in various scenario to obtain the most optimized reserved estimate that can minimize the risk of being unable to pay the insurance claim or even the risk of over allocating reserves that could pose profitability issue. The primary data used are the Australian domestic motor insurance claims from 2012 to 2017, obtained from Australian Prudential Regulation Authority (APRA). The dataset is then manipulated to have outliers. After calculating the estimation, the result is compared to assess the strength of the methods using Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) calculation. In conclusion, we found that the robust chain ladder reserving method works better in an outlying dataset. We also identify cases in which robust chain ladder are not appropriately used.

An Actuarial Comparison of General Business Insurance Loss Reserving: Evidence from Classical Chain Ladder and Cape-Cod Technical Provisions Numerical Techniques

The assets and liabilities of a general insurance underwriter constitutes two main variables usually adopted when evaluating the solvency requirements of a general insurance firm under which technical provisions form an unprecedented part of insurance liabilities. The technical provision of a general insurance business comprises provisions for unearned premiums and provisions for claims. The technical provisions specified under solvency II requirements asserts that the classical actuarial techniques for evaluating the best estimate for provisions in general business insurance obligations contains the run off triangles. The objective of this study are to (i) estimate the chain ladder reserve (ii) estimate the cape-cod reserve and (iii) compare the chain ladder with the cape-cod mathematical techniques with the disposition of estimating losses and technical provisions. These techniques evaluated through some run-off triangles can be adopted to estimate technical provisions for the outstanding claims. Computational evidence from our results over the periods considered revealed that despite the fact that the cape-cod technique is a mathematical variant of the chain ladder technique which seems less dependent on the variations of a single observation, the chain ladder reserve is numerically less than the corresponding cape-cod reserve and hence CLRESERVE = 18534.42 < CCRESERVE = 19123.84

ESTIMASI CADANGAN KLAIM PADA ASURANSI UMUM DENGAN METODE CHAIN LADDER

Based on the 2020 Insurance Statistic Data released by OJK, the ratio of gross claims to gross premiums has increased due to the growth of gross premiums followed by increasing claims paid. Thus, the insurance company is obliged to provides claim reserve that is important to be estimated appropriately, especially outstanding claim reserves. This is because outstanding claim reserves are needed to cover underpayment on future claims. One popular method to estimate outstanding claim reserves is the Chain Ladder method. This study aims to determine the results of the estimated outstanding claim reserves on general insurance using Mack’s CL method. CL method is a method to estimate claim reserves simply without satisfying certain distribution assumptions. This study uses incremental run-off triangle data taken from Weindofer's research article (2012) with an event period of 2005-2012 and a development period of 8 years. Based on the calculations in this study, an estimated outstanding claim reserve of USD 20,109.82 was obtained, meaning the funds that must be prepared amounted to USD 20,109.82 in 2013 by the general insurance company that owns the data studied. It also serves as a benchmark in the determination of claim reserves in the 2013 financial statements

Asymptotic theory for Mack's model

The distribution-free chain ladder reserving model by Mack (1993) belongs to the most popular approaches in non-life insurance mathematics. It was originally proposed to determine the first two moments of the reserve distribution. Together with a normal approximation, it is commonly applied to conduct statistical inference including the estimation of large quantiles of the reserve and determination of the reserve risk. However, for Mack's model, the literature lacks a rigorous justification of such a normal approximation for the reserve.In this paper, we propose a general stochastic framework which allows to derive asymptotic theory for Mack's model. For increasing number of accident years, we establish central limit theorems for the parameter estimators in Mack's model. In particular, these results enable us to derive also unconditional and conditional limiting distributions for the reserve. For this purpose, the reserve risk is split into two random parts that carry the process uncertainty and the estimation uncertainty, respectively. Unconditionally, but also when conditioning on either the whole observed loss triangle or on its diagonal, we show that the limiting distribution of the first part that corresponds to the process uncertainty will be usually non-Gaussian. When properly inflated, the second part corresponding to the estimation uncertainty is measurable with respect to the loss triangle and, unconditionally, turns out to be asymptotically non-Gaussian as well. By contrast, when conditioning only on the diagonal, this results in a Gaussian limit. As the process uncertainty part dominates asymptotically, this leads overall to a non-Gaussian limiting distribution for the reserve in both cases.These findings cast the common practice to use a normal approximation for the reserve in Mack's model into doubt. We illustrate our findings by simulations and show that our setup covers cases, where the limiting distributions of the reserve risk might deviate substantially from a Gaussian distribution.

Stochastic reserving using policyholder information via EM algorithm

In stochastic reserving, the incurred outstanding liabilities of general insurance companies result in incomplete claims because of truncation and censoring. It is necessary for insurance companies to predict liabilities in risk management. We propose a model that allows the incorporation of heterogeneity among policies, which is important for loss reserving. The incompleteness of observation data leads us to use expectation-maximization (EM) algorithm to obtain the maximum likelihood estimations of the parameters of the model. We also show that the deviation of loss reserving from the loss reserve weakly converges to a normal distribution at the rate m, where m is the size of the risk portfolio. A simulation study is conducted to compare the proposed method with the ones without policyholder’s information as well as obtained by chain ladder method and compare the convergence rates of EM algorithm and the direct maximization by Newton-Raphson method. We also analyse real-life health insurance data to illustrate the use of the method in practice.

ESTIMATION OF IBNR AND RBNS RESERVES USING RDC METHOD AND GAMMA GENERALIZED LINEAR MODEL

Estimation of claims reserves is a very important role for insurance companies because the information will be used to assess the insurance company’s ability to meet future claim payment obligations. In practice, claims reserves are divided into two Incurred but Not Reported (IBNR) and Reported but Not Settled (RBNS). Reserving by Detailed Conditioning (RDC) is one of the individual methods that can estimate claims reserves of both the IBNR and RBNS, which involves detailed condition so-called claim characteristics, and some information else so-called background variable. The result of estimating claims reserves using RDC with background variable is not stable because many combinate of calculation from each background variable. The purpose of this study is to overcome these problems, which we can combine RDC and Gamma Generalized Linear Model (GLM) as an effective method for estimating claims reserves. By using Bootstrapping Individual Claims Histories (BICH) method, the results show that estimation of claims reserves using RDC and Gamma GLM gives the fewest value of Mean Square Error of Prediction (MSEP) rather than RDC with Poisson GLM, RDC, and Chain Ladder. Where the smaller the value of the resulting MSEP estimate, the closer to the actual claim reserve value.

Comparison of Statistical Methods for Claims Reserve Estimation Using R Language

Stochastic methods of reserves estimation serve to assess the technical provisions of outstanding claims and forecast cash payments of claims in the coming years. The chain ladder model developed by Mack is the more prevalent model. The main deficiency in the chain-ladder model is that the chain-ladder model depends on the last observation on the diagonal. If this last observation is an outlier, this outlier will be projected to the ultimate claim. One of the possibilities to smooth outliers on the last observed diagonal is to robustify such observations, making use of the maximum likelihood estimation along with the common Loss Development Factor (LDF) curve fitting and Cape Cod (CC) techniques. This paper aims to highlight the advantages of using these methods for the best estimate of claims reserves in the Domestic Motor Third Party Liability portfolio. The maximum–likelihood parameter estimation and Chi-square test, are used to specify the probability distribution that best fits the data. Using the Standard Chain Ladder method, LDF, and CC method the claims reserve is calculated based on the run-off triangles of paid claims or the run-off triangles of the incurred claims. Many times, the projections based on the paid claims are different than the projections based on the incurred claims. The solution for this problem is the Munich Chain Ladder method.

An incremental loss ratio method using prior information on calendar year effects.

In a run-off triangle external factors can have a similar influence on all incremental losses of the same calendar year. This can distort the triangle such that reserving methods like chain ladder or the loss ratio method do not work properly. A very recent example of such an external factor is the Covid-19 pandemic. In many countries, the insurance industry is in the process of establishing market knowledge about the impact of the pandemic on premiums and losses. We extend the additive claims reserving model to allow for calendar year effects and develop a variant of the incremental loss ratio method (also known as the additive method) that can make use of such market knowledge. We derive formulas for the mean squared error of prediction and provide a detailed numerical example.Supplementary InformationThe online version contains supplementary material available at 10.1007/s13385-022-00315-3.

Micro-level prediction of outstanding claim counts based on novel mixture models and neural networks

Predicting the number of outstanding claims (IBNR) is a central problem in actuarial loss reserving. Classical approaches like the Chain Ladder method rely on aggregating the available data in form of loss triangles, thereby wasting potentially useful additional claims information. A new approach based on a micro-level model for reporting delays involving neural networks is proposed. It is shown by extensive simulation experiments and an application to a large-scale real data set involving motor legal insurance claims that the new approach provides more accurate predictions in case of non-homogeneous portfolios.

Robust Bayesian estimation and prediction in gamma-gamma model of claim reserves

The problem of robust Bayesian estimation of chain ladder (development) factors and Bayesian prediction of claim reserves is considered. Two different classes of priors (the classes, where parameters of a prior are not specified exactly and the class, where the prior cumulative distribution function is distorted) are presented. The oscillation (as a measure of robustness) of Bayes estimators and predictors of reserves, when priors are in the considered class, is calculated and the posterior regret Γ-minimax (PRGM) rules as optimal procedures are obtained. The numerical example compares different methods of the estimation of development factors and the calculation of claim reserves. The chain ladder estimators and predictors, exact Bayes estimators and predictors, PRGM estimators and predictors for aforementioned classes of priors and empirical credibility estimators and predictors are considered. It is shown that the variability of the expected value parameter of a prior has a greater impact on the oscillation of the Bayes estimators of the development factors and Bayes predictors of reserves than the variability of the shape parameter. The Bayes predictors are more robust with respect to the distortion of a prior c.d.f. than the fluctuation of the expected value parameter of a Gamma prior. A distortion of the shape of the prior c.d.f. has also a smaller impact on the value of PRGM estimators and predictors than the variability of the parameters of Gamma distribution. The difference between the Bayesian and chain ladder estimators (and predictors) depends mainly on the difference between the expected value parameter of the prior and the chain ladder estimator of development factor.