Claims Reserve Research Articles

Chain claims reserving methods in non-life insurance

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.

Segmented individual claim reserve estimation using BART refinement

We want to extend an individual claim reserving method proposed by [1] and also [2] by using segmented calculation. This method is an individual method of claims reserve estimation which involves detailed condition on claim characteristics in the calculation process. Data is divided into several segments according to combination of background variables. We then apply RDC method to find estimated IBNR and RBNS reserves for each segment. Bayesian Additive Regression Tree (BART) is used to refine the estimated reserves. This is because the estimation become unstable due to a lot of combination factors for each segment.

Prediction of Technical Reserves Based on Grey Model — GM(1,1): Evidence from Non-life Egyptian Insurance Market

Grey system theory is a mathematical technique used to predict data with known and unknown characteristics. The aim of our research is to forecast the future amount of technical reserves (outstanding claims reserve, loss ratio fluctuations reserve and unearned premiums reserve) up to 2029/2030. This study applies the Grey Model GM(1,1) using data obtained from the Egyptian Financial Supervisory Authority (EFSA) over the period from 2005/2006 to 2015/2016 for non-life Egyptian insurance market. We found that the predicted amounts of outstanding claims reserve and loss ratio fluctuations reserve are highly significant than the unearned premiums reserve according to the value of Posterior Error Ratio (PER).

A TREE-BASED ALGORITHM ADAPTED TO MICROLEVEL RESERVING AND LONG DEVELOPMENT CLAIMS

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.

Modelling Outstanding Claims with Mixed Compound Processes in Insurance

In general insurance, measuring the uncertainty of future loss payments and estimating the claims reserve are primary goals of actuaries. To deal with these tricky tasks, a broad literature is available on deterministic and stochastic approaches, most of which aims at straightforwardly modelling the overall claims reserve. In this paper by an extended, very general and reproducible case-study, we analyze the reserving process by attributing to each cell of the lower part of the run-off triangle a Compound mixed Poisson Process, calibrated upon both the numbers of claims and future average costs and considering as well the dependence among incremental claims. We provide analytically the moments of both incremental payments and the total reserve. Furthermore, we accordingly consider the probability distribution of the claims reserve, which is necessary for the assessment of the Risk Reserve capital requirement in a Solvency II framework. To test the impact of the model under different scenarios, insurers and lines of business, the case study is thoroughly analyzed by exploiting the Fisher-Lange average cost method.

A Multivariate Evolutionary Generalised Linear Model Framework with Adaptive Estimation for Claims Reserving

In this paper, we develop a multivariate evolutionary generalised linear model (GLM) framework for claims reserving, which allows for dynamic features of claims activity in conjunction with dependency across business lines to accurately assess claims reserves. We extend the traditional GLM reserving framework on two fronts: GLM fixed factors are allowed to evolve in a recursive manner, and dependence is incorporated in the specification of these factors using a common shock approach. We consider factors that evolve across accident years in conjunction with factors that evolve across calendar years. This two-dimensional evolution of factors is unconventional as a traditional evolutionary model typically considers the evolution in one single time dimension. This creates challenges for the estimation process, which we tackle in this paper. We develop the formulation of a particle filtering algorithm with parameter learning procedure. This is an adaptive estimation approach which updates evolving factors of the framework recursively over time. We implement and illustrate our model with a simulated data set, as well as a set of real data from a Canadian insurer.

Individual Claims Reserving in Creditor Protection Insurance Using Machine Learning

In the context of individual claims reserving in non-life insurance, a new perspective involving machine learning techniques was recently introduced. We focused on credit insurance which, despite being seldom explored, can represent an interesting challenge for machine learning techniques because of its volatile nature, sensitive to economic trends. In a framework where insurance undertakings are collecting an increasing amount of data, methods like Neural Networks and Support Vector Machines could provide a valid alternative to traditional reserving techniques, offering an easy way to include macro-economic information in the estimation process. While recent machine learning literature have focused mainly on case reserving and on analysis of loss development triangles, in this work we provide a complete evaluation of each component of the Claims Reserve in a granular sense and we compare, in terms of both bias and variability, their results with Generalised Linear Models, which can be considered a standard actuarial tool.

Log-Normal or Over-Dispersed Poisson?

Although both over-dispersed Poisson and log-normal chain-ladder models are popular in claim reserving, it is not obvious when to choose which model. Yet, the two models are obviously different. While the over-dispersed Poisson model imposes the variance to mean ratio to be common across the array, the log-normal model assumes the same for the standard deviation to mean ratio. Leveraging this insight, we propose a test that has the power to distinguish between the two models. The theory is asymptotic, but it does not build on a large size of the array and, instead, makes use of information accumulating within the cells. The test has a non-standard asymptotic distribution; however, saddle point approximations are available. We show in a simulation study that these approximations are accurate and that the test performs well in finite samples and has high power.

Kaplan-Meier Survival Analysis in Estimating the Number of Earned Exposure Units

The estimated number of earned exposure units can help corporate executives of auto insurance company in calculating their own individual claim reserves. We conduct the estimation of this number of earned exposure units by using Kaplan-Meier survival analysis to generate the survival table. The generated survival table were then divided to be 9 risk groups based on the issuance of Financial Services Authority of Indonesia No. 6/SEOJK.05/2017 and the duration of auto insurance coverage in Indonesia. We used Root Mean Squared of Error (RMSE) as one of error measurement of the survival model. Meanwhile, a series of one-sample test with log-rank weighted function were performed for each risk group to demonstrate the goodness of fit. The estimation generated by using the survival table produce more conservative results compared to the reality. This gives assurance for one of the auto insurance company in Indonesia to use the expected earned exposure units as a basis to calculate the amount of unit that have risk to suffer a partial loss claim but still support the company in optimizing their resources.

Stochastic Claims Reserving in Insurance Using Random Effects

Estimation of claims reserves, which should be held by the insurer so as to be able to meet expected future claims arising from policies currently in force and policies written in the past, presents an important task for insurance companies to predict their liabilities. A common approach to the reser-ving problem is based on generalized linear models (GLM). In this article, the application of genera-lized linear mixed models (GLMM) - an extension of the GLM - for estimation of the loss reserves is shown. Since the GLMM allows incorporating a random effect instead of several fixed effects corresponding to the accident years as in case of the GLM, volatility of the prediction is reduced. This allows more flexible risk valuation, which is a crucial element of risk management and capital allocation practices of non-life insurers. A real data example together with diagnostics for the model selection are provided as an illustration of the potential benefits of the presented approach.

Robust Bayesian estimation and prediction of reserves in exponential model with quadratic variance function

The exponential families with quadratic variance function, conjugate families of priors and square loss function is applied to the prediction of claim reserves. The robustness with respect to the priors is considered. The uncertainty of the prior information is modeled by two different classes of priors. The posterior regret Γ-minimax estimators and predictors are constructed.

Valuation of Non-Life Liabilities from Claims Triangles

This paper provides a complete program for the valuation of aggregate non-life insurance liability cash flows based on claims triangle data. The valuation is fully consistent with the principle of valuation by considering the costs associated with a transfer of the liability to a so-called reference undertaking subject to capital requirements throughout the runoff of the liability cash flow. The valuation program includes complete details on parameter estimation, bias correction and conservative estimation of the value of the liability under partial information. The latter is based on a new approach to the estimation of mean squared error of claims reserve prediction.

Bootstrapping the Ultimate Claims of Cumulative Claims Payments and Incurred Losses Data Using Kalman-Filter Theory

The prediction of outstanding loss liabilities for non-life run-off portfolios and the quantification of the prediction error is one of the most important actuarial tasks in non-life insurance. In this paper we consider this prediction problem in a bivariate context. More precisely, we derive the predictive bootstrap distribution of the aggregated claims reserve based on cumulative claims payments and incurred losses data using Kalman-filter theory. With the predictive bootstrap distribution we are able to calculate all risk measures such as Value-at-Risk, Expected-Shortfall or Conditional-Tail-Expectation. An example is given at the end with a calculation of the bootstrap distribution and various risk measures are presented.

On Comparison of Stochastic Reserving Methods with Bootstrapping

We consider the well-known stochastic reserve estimation methods on the basis of generalized linear models, such as the (over-dispersed) Poisson model, the gamma model and the log-normal model. For the likely variability of the claims reserve, bootstrap method is considered. In the bootstrapping framework, we discuss the choice of residuals, namely the Pearson residuals, the deviance residuals and the Anscombe residuals. In addition, several possible residual adjustments are discussed and compared in a case study. We carry out a practical implementation and comparison of methods using real-life insurance data to estimate reserves and their prediction errors. We propose to consider proper scoring rules for model validation, and the assessments will be drawn from an extensive case study.

Fitting Finite Mixtures of Generalized Linear Regressions on Motor Insurance Claims

The aim of this study is to determine the best mixture model for claim amount from a comprehensive insurance policy portfolio and use the model to estimate the expected claim amount per risk for the coming calendar year. The claims data were obtained from the motor insurance office of one of the top business insurance companies in Ghana. The data consists of one thousand (1,000) claim amounts from January 2012 to December 2014. The expectation-maximization (EM) algorithm within a maximum likelihood framework was used to estimate the parameters of four mixture models namely the Heterogeneous Normal-Normal, Homogeneous Normal-Normal, Pareto-Gamma and Gamma-Gamma. These mixture models were fitted to the claims data and measures of goodness-of-fit (AIC and BIC) were used to determine the best mixture model. The Heterogeneous Normal-Normal mixture distribution was the appropriate model for the motor insurance claims data due to the least AIC. The estimated expected claims amount for the coming calendar year (2015) from the model was GHS 877.672 per risk. This in a way may inform decision makers as to the kind of anticipated reserves for future claims.

A comparative analysis of outstanding claim reserves

A comparative analysis of outstanding claim reserves

Historical Origin of the Cape Cod Claims Reserving Method

The Cape Cod Claims Reserving Method was invented in 1983 through practical work at Swiss Re and made public in the Summer School of the Swiss Actuarial Association (Leysin 1983).The method is now quite frequently used but the only written record are mimeographed notes of this Summer School. This article edits these mimeographed notes in a more easily accessible form.

Aggregate Discounted Warranty Cost Forecast for a New Product Considering Stochastic Sales

Most commercial products are sold with a warranty. Product repairs during the warranty period are often free of charge, and contribute significantly to the costs of a manufacturer. Estimation of the warranty costs is important for the manufacturer to prepare sufficient warranty reserves for future claims. Because products are often sold to customers intermittently, the total number of sold units under warranty varies over time, which presents difficulties in forecasting the warranty costs over time. In this study, we consider the stochastic sales process, and derive the expectation and variance of the aggregate discounted warranty costs within a given period of time. By taking the variation of the warranty costs into consideration, the result can be used in the preparation of a conservative warranty reserve for a new product. The discounted life-cycle warranty cost is a special case of our model, and it can also be determined from our result. Numerical results show the applicability of our model in estimating periodic discounted warranty costs, and preparing both short-term and long-term warranty reserves.

Stochastic model to evaluate the fair value of motor third-party liability under the direct reimbursement scheme and quantification of the capital requirement in a Solvency II perspective

As commonly known, to evaluate the claims reserve (otherwise known as the provision for outstanding claims), the loss adjuster uses as a first component the claims reserve given by the sum of the estimated provision for each outstanding claim (known as case reserve). Traditional statistical-actuarial methods are used to control and/or asseverate the evaluation and recent developments have tended to ensure that these enable an independent assessment of the claims reserve. In some European countries, a large subset of motor liability claims is managed within a direct reimbursement (DR) scheme. In Italy, the introduction of the direct compensation CARD system for third-party liability insurance has resulted in greater attention in the use of these traditional methods due to the heterogeneity of the data available for evaluations. This paper presents the results of a study undertaken to define a calculation method that, using the different assumptions that describe the evolution of settlement mechanisms, is able to quantify the claims reserve. The proposed methodology reduces the loss adjuster’s discretion in applying statistical methods since all assumptions must be made explicit and can hence be monitored and controlled. Furthermore, a stress test can be performed on all the parameters that influence the settlement and thus the claims reserve. Finally, in a backtesting perspective, the proposed methodology enables an ex-post analysis of actual cash flow deviations compared to expected values, identifying the variables that lead to these differences. In particular, a calculation method is presented that using the different assumptions describing the evolution of the settlement of different claim handling procedures (Non-Card, Card, Handler Forfait and Debtor Forfait) is able to quantify the claims reserve. Via simulations, future payments, the expected value of the claims reserve and some indicators of variability are also estimated. The numerical application allows comparing the results obtained with those deriving from the application of traditional statistical methods.The problem of aggregating the four claim handling procedures is dealt with by using copulas with the goal of building a single distribution of the aggregate claims reserve. Furthermore, in a Solvency II perspective, the capital requirement is determined against the reserve risk based on the internal model proposed and is compared with the standard formula proposed by EIOPA.

The Prediction of Non-Life Claim Reserves under Inflation<br/>—An Analysis including Diagonal Effects

The extraction of various reserves is one of the most important measures that guarantee insurance companies’ solvency. Accurate assessment of non-life insurance claim reserves needs to consider the volatility risks of inflation. This paper presents a stochastic model of claim reserves including inflation factor and diagonal effects. By applying this model, we can predict the values of the claim reserves and evaluate predicting risks. Through analyzing actual data and using the bootstrap method, we can compare Bornhuetter-Ferguson method involving diagonal effects with chain ladder method. It is shown that the former is more efficient and robust than the latter.