Chain Ladder Method 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.

Claim reserving via inverse probability weighting: a micro-level Chain-Ladder method

Claim reserving via inverse probability weighting: a micro-level Chain-Ladder method

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.

Calculating Insurance Claim Reserves with an Intuitionistic Fuzzy Chain-Ladder Method

Calculating Insurance Claim Reserves with an Intuitionistic Fuzzy Chain-Ladder Method

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.

Claims Reserving with a Robust Generalized Additive Model

In the actuarial literature, many existing stochastic claims-reserving methods ignore the excessive effects of outliers. In practice, however, these outlying observations may occur in the upper triangle and can have a nontrivial and undesirable influence on the existing reserving models. In this article, we consider the situation when outliers of claims are present in the upper triangle. We demonstrate that the model fitting and prediction results of the classical chain-ladder method can be substantially affected by these outliers. To mitigate this negative effect, we propose a robust generalized additive model (GAM). An associated robust bootstrap based on stratified sampling is also developed to obtain a more reliable predictive bootstrap distribution of outstanding claims. Using both simulation examples and real data, we compare our proposed robust GAM with nonrobust counterparts and robust GLM. We demonstrate that the robust GAM provides comparable results with those of other models when outliers are not present and that the robust GAM demonstrates significant improvements in estimation accuracy and efficiency when outliers are present.

Estimating IBNR claim reserves using Gaussian Fuzzy Numbers

The study aimed to propose a new approach to the chain-ladder method using for that Gaussian Fuzzy Numbers. For that, the text introduces concepts and establishes new perspectives that allow not just the use of this kind of fuzzy number in the claim estimation context but also in other areas of knowledge, corroborating, in that way, to the expansion of the adoption of fuzzy logics in a general sense. The results indicates that the adoption of the proposed method offers huge benefits when compared to the traditional approach and previous works exploring other kind of fuzzy numbers.
 Keywords: claim reserves; fuzzy logic; fuzzy numbers; IBNR.

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

THE RELIABILITY OF RESERVES VALUATION IN INSURANCE COMPANIES

Starting from the theory of probabilities, which represents an attempt to investigate uncertainty, insurance companies must calculate their insurance premiums in such a way as to cover all their operational expenses and obtain the expected benefit, preserving the principle of equity and solidarity. In commercial insurance, statistical research plays a special role in estimating the level of insurance activity and its prospects. For this purpose, the events that take place in insurance are measured, ordered, systematized and aggregated through observation (collection), processing and analysis. Estimating the risk and the insurer’s obligations based on inadequate or incorrect data is an extremely dangerous situation. Therefore, it is extremely important for the insurer to establish the best possibility of observing and using the data. Basing premium rates and reserves is an important activity for insurance companies. If insurers do not accurately set premium rates that reflect the size of the risk, they may suffer losses due to the financial imbalance created between premiums and indemnities or due to adverse selection. The actuary deals with this within the insurance company, using various actuarial statistical methods. The 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. 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. The substantiation of technical reserves must be based on specific methods because there is a possibility that two insurers may use different calculation techniques for similar obligations and obtain totally different results, thus disrupting profitability and financial soundness.

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

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.

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.

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.

A robust random coefficient regression representation of the chain-ladder method

AbstractIt is well known that the presence of outliers can mis-estimate (underestimate or overestimate) the overall reserve in the chain-ladder method, when we consider a linear regression model, based on the assumption that the coefficients are fixed and identical from one observation to another. By relaxing the usual regression assumptions and applying a regression with randomly varying coefficients, we have a similar phenomenon, i.e., mis-estimation of the overall reserves. The lack of robustness of loss reserving regression with random coefficients on incremental payment estimators leads to the development of this paper, aiming to apply robust statistical procedures to the loss reserving estimation when regression coefficients are random. Numerical results of the proposed method are illustrated and compared with the results that were obtained by linear regression with fixed coefficients.

Collective reserving using individual claims data

The aim of this paper is to operationalize claims reserving based on individual claims data. We design a modeling architecture that is based on six different neural networks. Each network is a separate module that serves a certain modeling purpose. We apply our architecture to individual claims data and predict their settlement processes on a monthly time grid. A proof of concept is provided by benchmarking the resulting claims reserves with the ones received from the classical chain-ladder method which uses much coarser (aggregated) data.

Implementation of Gaussian Process Regression in Estimating Motor Vehicle Insurance Claims Reserves

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.