Practical considerations in claims inflation estimation

Assessing Inflation Risk in Non-Life Insurance

Assessing inflation risk in non-life insurance

Typically, non-life insurance claims data is studied in claims development triangles which display the two time axes accident years and development years. Most stochastic claims reserving models assume independence between different accident years. Therefore, such models fail to model claims inflation appropriately, because claims inflation acts on all accident years simultaneously. We introduce a Bayes chain ladder reserving model which enables us to model claims inflation. In this model we derive analytical formulas for the posterior distribution, the claims reserves and their prediction uncertainty.

An incentive contracting approach is used to characterize optimal contracts when insured individuals possess private information about their losses and are able to misrepresent permanently their loss magnitudes by engaging in the falsification of claims. We demonstrate that efficient agreements necessarily induce some falsification but that the extent of such claims inflation is mitigated partially by an indemnification schedule that overcompensates small losses while overpaying larger ones. The differential costs of generating insurance claims through falsification provide an avenue by which the heterogencous insureds can credibly signal their underlying losses and are exploited in an optimal contract to implement loss‐contingent insurance payments.

The development of private health insurance in Malaysia: A case study analysis exploring its influence on financial risk protection

Dependence Modeling in Multivariate Claims Run-Off Triangles

In today’s world society, the proliferation of claims could be seen as a problematic consequence of functional differentiation and modern individualism: everyone could potentially be included in every subsystem of society (economy, law, politics, etc.), but has to build his or her own personal identity through decisions. Claims are then the result of the attempts to be individual (self-determined, specific, different), i.e. to respond to contingency and complexity. While the Western tradition socially legitimates the claim to be different from others, this legacy seems to be challenged today. The paper analyses four emerging tendencies relating to claims to protection and inclusion based not on the individual per se, but on specific memberships, on the one hand, and on the insistence on affectivity, on the other. The hypothesis is that these claims reflect the difficulty of responding to structural change in a society dominated by contingency and uncertainty.

A central issue in claims reserving is the modelling of appropriate dependence structures. Most classical models cannot cope with this task. We define a multivariate log-normal model that allows to model both, dependence between different sub-portfolios and dependence within sub-portfolios such as claims inflation. In this model we derive closed form solutions for claims reserves and the corresponding prediction uncertainty.

In almost all stochastic claims reserving models one assumes that accident years are independent. In practice this assumption is violated most of the time. Typical examples are claims inflation and accounting year effects that influence all accident years simultaneously. We study a Bayesian chain ladder model that allows for accounting (calendar) year effects modeling. A case study of a general liability dataset shows that such accounting year effects contribute substantially to the prediction uncertainty and therefore need a careful treatment within a risk management and solvency framework.

Claims 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 theh-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.

ABSTRACTThis paper examines the chain-ladder technique using the recently developed theory for age-period-cohort models. The theory was set out by Kuang et al. (2008a), and we believe that it has some significant implications for claims reserving and the chain-ladder technique. This paper applies the age-period-cohort model using the over-dispersed Poisson framework, and examines a number of experiments in order to understand better how the chain-ladder technique deals with calendar year effects. The conclusions from these investigations are that the basic chain-ladder technique may have some fundamental difficulties in many circumstances. We would therefore recommend that it should be used with caution, and that the data are examined in detail before any projections are made. This has particular importance in the context of solvency calculations since the chain-ladder technique can impose some specific patterns into the projections.

Objective:This study evaluated differences in medical costs associated with clinical end-points from randomized clinical trials that compared the new oral anticoagulants (NOACs), dabigatran, rivaroxaban, apixaban, and edoxaban, to standard therapy for treatment of patients with venous thromboembolism (VTE).Research design and methods:Event rates of efficacy and safety end-points from the clinical trials (RE-COVER, RE-COVER II, EINSTEIN-Pooled, AMPLIFY, Hokusai-VTE trial) were obtained from published literature. Incremental annual medical costs among patients with clinical events from a US payer perspective were obtained from the literature or healthcare claims databases and inflation adjusted to 2013 costs. Differences in total medical costs associated with clinical end-points for the NOACs vs standard therapy were then estimated. One-way and Monte Carlo sensitivity analyses were carried out.Results:A lower rate of major bleedings was associated with use of any of the NOACs vs standard therapy. Except for dabigatran, use of NOACs was also associated with a lower rate of recurrent VTE/death. As a result of the reduction in clinical event rates, the overall medical cost differences were −$146, −$482, −$918, and −$344 for VTE patients treated with dabigatran, rivaroxaban, apixaban, and edoxaban, respectively, vs patients treated with standard therapy.Conclusions:When any of the four NOACs are used instead of standard therapy for acute VTE, treatment medical costs are reduced. Apixaban is associated with the greatest reduction in medical costs, which is driven by medical cost reductions associated with both efficacy and safety end-points. Further evaluation may be needed to validate these results in the real-world setting.

Obstetric claims inflation is increasing the cost of covering obstetric risk. This is leading to obstetric risk avoidance by those offering insurance and by practitioners who do not perform enough deliveries to cover the cost of obstetric risk indemnity. By the end of the decade indemnifying obstetric risk will probably be too expensive for doctors in private practice. Non-indemnified doctors will be unable or unwilling to do private deliveries; however, women will still fall pregnant and require delivery. These women will inevitably be forced to deliver in provincial facilities, shifting the workload and liability to the state.

There exist a few intuitive and theoretically interesting reinsurance contracts that are akin to excess‐of‐loss treaties, but refer to the larger claims in a portfolio. An unlimited excess‐of‐loss contract cuts off each claim at a fixed, nonrandom retention. A variant of this principle is ECOMOR reinsurance where the priority is put at the ( r + 1)th largest claim so that the reinsurer pays that part of the r largest claims that exceed the ( r + 1)th largest claim. Compared to unlimited excess‐of‐loss reinsurance, ECOMOR reinsurance has an advantage that gives the reinsurer protection against unexpected claims inflation if the claim amounts increase, then the priority will also increase. A related and slightly simpler reinsurance form is largest claims reinsurance that covers the r largest claims but without a priority. The article highlights some of the theoretical results that can be obtained for the case where the total volume in the portfolio is large. In spite of their conceptual appeal, largest claims type reinsurance are rarely applied in practice. The discussion hints at some of the possible reasons for this lack of popularity.

Setting the Claims Inflation Assumptions