Unallocated loss adjustment expense reserving

In non-life insurance, the provision for outstanding claims (the claims reserve) should include future loss adjustment expenses, i.e. administrative expenses to settle the claims, and therefore we have to estimate the expected Unallocated Loss Adjustment Expenses (ULAE) – expenses that are not attributable to individual claims, such as salaries at the claims handling department. The ULAE reserve has received little attention from European actuaries in the literature, supposedly because of the lack of detailed data for estimation and evaluation. Having good estimation procedures will, however, become even more important with the introduction of the Solvency II regulations, which require unbiased estimation of future cash flows for all expenses. We present a model for ULAE at the individual claim level that includes both fixed and variable costs. This model leads to an estimate of the ULAE reserve at the aggregate (line-of-business) level, as demonstrated in a numerical example from a Swedish non-life insurer.     

Non-parametric and parametric bootstrap techniques for age-to-age development factor methods in stochastic claims reserving

In the literature, one of the main objects of stochastic claims reserving is to find models underlying the chain-ladder method in order to analyze the variability of the outstanding claims, either analytically or by bootstrapping. In bootstrapping these models are used to find a full predictive distribution of the claims reserve, even though there is a long tradition of actuaries calculating the reserve estimate according to more complex algorithms than the chain-ladder, without explicit reference to an underlying model. In this paper we investigate existing bootstrap techniques and suggest two alternative bootstrap procedures, one non-parametric and one parametric, by which the predictive distribution of the claims reserve can be found for other age-to-age development factor methods than the chain-ladder, using some rather mild model assumptions. For illustration, the procedures are applied to three different development triangles.     

Separation of small and large claims on the basis of collective models

This paper is inspired by two papers of Riegel who proposed to consider the paid and incurred loss development of the individual claims and to use a filter in order to separate small and large claims and to construct loss development squares for the paid or incurred small or large claims and for the numbers of large claims. We show that such loss development squares can be constructed from collective models for the accident years. Moreover, under certain assumptions on these collective models, we show that a development pattern exists for each of these loss development squares, which implies that various methods of loss reserving can be used for prediction and that the chain ladder method is a natural method for the prediction of future numbers of large claims.     

Micro-level stochastic loss reserving for general insurance

The vast literature on stochastic loss reserving concentrates on data aggregated in run-off triangles. However, a triangle is a summary of an underlying data-set with the development of individual claims. We refer to this data-set as ‘micro-level’ data. Using the framework of Position Dependent Marked Poisson Processes) and statistical tools for recurrent events, a data-set is analyzed with liability claims from a European insurance company. We use detailed information of the time of occurrence of the claim, the delay between occurrence and reporting to the insurance company, the occurrences of payments and their sizes, and the final settlement. Our specifications are (semi)parametric and our approach is likelihood based. We calibrate our model to historical data and use it to project the future development of open claims. An out-of-sample prediction exercise shows that we obtain detailed and valuable reserve calculations. For the case study developed in this paper, the micro-level model outperforms the results obtained with traditional loss reserving methods for aggregate data.     

Another pragmatic loss reserving method or Bornhuetter-Ferguson revisited

Abstract

The efficiency of an approximate credibility method for predicting outstanding claims in reinsurance, is analysed. The advantage of the approximate method is, that it does not require exact knowledge of the model's second order moments.     

The role of epistemic policies in regulatory science: scientific substantiation of health claims in the European Union

This paper presents an analysis of the concept of scientific substantiation in European health claims regulation. It focuses on the controversies about the demand for the establishment of cause-and-effect relationships between food consumption and health outcomes in claim substantiation. Our analysis, on the basis of regulatory and scientific documents, identifies two opposing views about the aims of health claims regulation. Each of these two stances links certain regulatory objectives with specific epistemic policies, that is particular sets of scientific methodology, criteria, and procedure. The regulators, in selecting a demanding evidentiary approach based on a hierarchy of methodologies that requires causal data for substantiation of claims, give priority to preventing the authorization of false claims. The opposing view, espoused by the critics of this approach, opts for less demanding requirements for substantiation, implying the market availability of a wider range of products with health claims that may provide individual as well as public health benefits. We argue that one of the objectives that underlie the European regulators’ demand for causal data is to protect their own credibility, by trying to isolate them from value-laden debates about the limitations of scientific methodologies, as well as the societal and policy implications of regulatory decision-making.     

Continuous chain-ladder with paid data

We introduce a continuous-time framework for the prediction of outstanding liabilities, in which chain-ladder development factors arise as a histogram estimator of a cost-weighted hazard function running in reversed development time. We use this formulation to show that under our assumptions on the individual data chain-ladder is consistent. Consistency is understood in the sense that both the number of observed claims grows to infinity and the level of aggregation tends to zero. We propose alternatives to chain-ladder development factors by replacing the histogram estimator with kernel smoothers and by estimating a cost-weighted density instead of a cost-weighted hazard. Finally, we provide a real-data example and a simulation study confirming the strengths of the proposed alternatives.     

Improved approximations for the aggregate claims distribution of a life insurance portfolio

Abstract

In an earlier paper the author derived a recursion formula which permits the exact computation of the aggregrate claims distribution in the individual life model. This exact procedure requires of course more computing time than approximative methods such as Kornya's algorithm, which seemed to be the best compromise between accuracy and computational effort. In the present paper it is shown that, to save time, the exact formula can be used in an approximative way and that the corresponding error bound is smaller than the one of the Kornya-type approximations.     

索赔准备金评估的非线性分层增长曲线模型研究

考虑损失流量三角形中同一事故年的损失随时间反复观测的纵向特征,将损失流量三角形视为分层数据,结合损失进展的增长曲线,提出了关于索赔准备金评估的两种非线性分层增长曲线模型,并应用R软件对精算实务中的实例给出了数值分析。提出的非线性分层模型为考虑多个事故年的损失进展建模提供了一种自然灵活的框架,使得建立的模型易于理解,同时在分层建模中纳入了增长曲线,也有效避免了尾部进展因子的选定问题。     

分配结构与潜在效率：剩余索取权分割模型——基于剩余控制权与权威排序的设计

剩余控制权有转换为剩余索取权的动机。现实的剩余索取权分割与剩余控制权结构之间并不存在稳定的匹配关系,权威排序是影响剩余控制权转向剩余索取权的重要变量。据此构建剩余索取权分割模型,研究分配结构对有效剩余控制权与有效剩余索取权的影响。结果表明,若权威排序至少为三级,剩余索取权分割主体的趋利选择,倾向于减少有效剩余控制权与有效剩余索取权;以剩余控制权为基础的剩余索取权分割结构,存在未实现的潜在效率。调整分配结构,是“激发”潜在效率的可能途径。     

De skandinaviske Aktuarforeningers Virksomhed i 1925

Abstract

Statistical extreme value theory provides a flexible and theoretically well motivated approach to the study of large losses in insurance. We give a brief review of the modem version of this theory and a “step by step” example of how to use it in large claims insurance. The discussion is based on a detailed investigation of a wind storm insurance problem. New results include a simulation study of estimators in the peaks over thresholds method with Generalised Pareto excesses, a discussion of Pareto and lognormal modelling and of methods to detect trends. Further results concern the use of meteorological information in the wind storm insurance and, of course, the results of the study of the wind storm claims.     

Corporate stakeholders,corporate valuation and ESG

In addition to explicit contracts, corporations issue their stakeholders implicit claims, including fair treatment of employees and the promise of continuing service to customers. Corporate value is created by selling these implicit claims for more than it costs to honour them. Recently, a new class of non-investor stakeholders, related to environmental, social and governance (ESG) issues, has arisen. Although many ESG advocates stress their role in creating shareholder value, they do not explain how this value creation occurs. This paper shows that implicit claims provide a critical link that ties non-investor stakeholders and ESG to shareholder value, both its creation and its possible destruction.     

Interest rate option pricing with volatility humps

This paper develops a simple model for pricing interest rate options when the volatility structure of forward rates is humped. Analytical solutions are developed for European claims and efficient algorithms exist for pricing American options. The interest rate claims are priced in the Heath-Jarrow-Morton paradigm, and hence incorporate full information on the term structure. The structure of volatilities is captured without using time varying parameters. As a result, the volatility structure is stationary. It is not possible to have all the above properties hold in a Heath Jarrow Morton model with a single state variable. It is shown that the full dynamics of the term structure is captured by a three state Markovian system. Caplet data is used to establish that the volatility hump is an important feature to capture. This revised version was published online in June 2006 with corrections to the Cover Date.     

巨灾失踪保险理赔问题

伴随巨灾的频发,巨灾失踪人员的保险理赔问题已成为保险业亟待解决的课题。巨灾失踪人员的保险理赔面临哪些困境,保险业应作何反思,并该如何应对。本文结合相关法律规定及保险契约约定,对上述问题进行分析,并提出对策。     

Robust bootstrap procedures for the chain-ladder method

Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic algorithm. To include a stochastic component one may apply generalized linear models to the run-off triangles based on past claims data. Analytical expressions for the standard deviation of the resulting reserve estimates are typically difficult to derive. A popular alternative approach to obtain inference is to use the bootstrap technique. However, the standard procedures are very sensitive to the possible presence of outliers. These atypical observations, deviating from the pattern of the majority of the data, may both inflate or deflate traditional reserve estimates and corresponding inference such as their standard errors. Even when paired with a robust chain-ladder method, classical bootstrap inference may break down. Therefore, we discuss and implement several robust bootstrap procedures in the claims reserving framework and we investigate and compare their performance on both simulated and real data. We also illustrate their use for obtaining the distribution of one year risk measures.     

Lognormal Mixed Models for Reported Claims Reserves

Abstract

Traditional claims-reserving techniques are based on so-called run-off triangles containing aggregate claim figures. Such a triangle provides a summary of an underlying data set with individual claim figures. This contribution explores the interpretation of the available individual data in the framework of longitudinal data analysis. Making use of the theory of linear mixed models, a flexible model for loss reserving is built. Whereas traditional claims-reserving techniques don’t lead directly to predictions for individual claims, the mixed model enables such predictions on a sound statistical basis with, for example, confidence regions. Both a likelihood-based as well as a Bayesian approach are considered. In the frequentist approach, expressions for the mean squared error of prediction of an individual claim reserve, origin year reserves, and the total reserve are derived. Using MCMC techniques, the Bayesian approach allows simulation from the complete predictive distribution of the reserves and the calculation of various risk measures. The paper ends with an illustration of the suggested techniques on a data set from practice, consisting of Belgian automotive third-party liability claims. The results for the mixed-model analysis are compared with those obtained from traditional claims-reserving techniques for run-off triangles. For the data under consideration, the lognormal mixed model fits the observed individual data well. It leads to individual predictions comparable to those obtained by applying chain-ladder development factors to individual data. Concerning the predictive power on the aggregate level, the mixed model leads to reasonable predictions and performs comparable to and often better than the stochastic chain ladder for aggregate data.     

A data set for modeling claims processes—TSA claims data

This data insight highlights the Transportation Security Administration (TSA) claims data as an underused data set that would be particularly useful to researchers developing statistical models to analyze claim frequency and severity. Individuals who have been injured or had items damaged, lost or stolen may make a claim for losses to the TSA. The federal government reports information on every claim from 2002 to 2017 at https://www.dhs.gov/tsa-claims-data . Information collected includes claim date and type and site as well as closed claim amount and disposition (whether it was approved in full, denied, or settled. We provide summary statistics on the frequency and the severity of the data for the years 2003 to 2015. The data set has several unique features including severity is not truncated (there is no deductible), there are significant mass points in the severity data, and the frequency data shows a high degree of auto correlation if compiled on a weekly basis, and substantial frequency mass points at zero for daily data.     

The performance of insolvency prediction and credit risk models in the UK: A comparative study

Theoretically-driven, market-based contingent claims models have recently been applied to the field of corporate insolvency prediction in an attempt to provide the art with a theoretical methodology that has been lacking in the past. Limited studies have been carried out in order directly to compare the performance of these models with that of their accounting number-based counterparts. We use receiver operating characteristic curves to assess the efficacy of thirteen selected models using, for the first time, post-IFRS UK data; and investigate the distributional properties of model efficacy. We find that the efficacy of the models is generally less than that reported in the prior literature; but that the contingent claims models outperform models which use accounting numbers. We also obtain the counter-intuitive finding that predictions based on a single variable can be as efficient as those which are based on models which are far more complicated – in terms of variable variety and mathematical construction. Finally, we develop and test a naïve version of the down-and-out-call barrier option model for insolvency prediction and find that, despite its simple formulation, it performs favourably compared alongside other contingent claims models.     

A Parimutuel Market Microstructure for Contingent Claims

Parimutuel principles are widely used as an alternative to fixed odds gambling in which a bookmaker acts as a dealer by quoting fixed rates of return on specified wagers. A parimutuel game is conducted as a call auction in which odds are allowed to fluctuate during the betting period until the betting period is closed or the auction ‘called’. The prices or odds of wagers are set based upon the relative amounts wagered on each risky outcome. In financial microstructure terms, trading under parimutuel principles is characterised by (1) call auction, non‐continuous trading; (2) riskless funding of claim payouts using the amounts paid for all of the claims during the auction; (3) special equilibrium pricing conditions requiring the relative prices of contingent claims equal the relative aggregate amounts wagered on such claims; (4) endogenous determination of unique state prices; and (5) higher efficiency. Recently, a number of large investment banks have adopted a parimutuel mechanism for offering contingent claims on various economic indices, such as the US Nonfarm payroll report and Eurozone Harmonised inflation. Our paper shows how the market microstructure incorporating parimutuel principles for contingent claims which allows for notional transactions, limit orders, and bundling of claims across states is constructed. We prove the existence of a unique price equilibrium for such a market and suggest an algorithm for computing the equilibrium. We also suggest that for a broad class of contingent claims, that the parimutuel microstructure recently deployed offers many advantages over the dominant dealer and exchange continuous time mechanisms.     

制约车险理赔服务质量的因素浅析

随着机动车辆保险保障范围的逐步扩大，广大消费者对保险的售后服务即车辆出险后的理赔工作提出越来越高的要求，而作为经营主体的各家保险公司由于营业网点、人员素质、产品特色、销售渠道等不同，服务水平参差不齐。