Description: The estimation of adequate reserves for outstanding claims is one of the main activities of actuaries in property/casualty insurance. The need to estimate future claims has led to the development of many loss reserving techniques. This paper is about the situation that occurs in claims reserving when there are negative values in the development triangle of incremental claim amounts. Typically, these negative values will be the result of salvage recoveries, payments from third parties, total or partial cancellation of outstanding claims due to initial overestimation of the loss or to possible favorable jury decision in favor of the insurer, rejection by the insurer, or just plain errors. Some of the traditional methods of claims reserving, such as the chain-ladder technique, may produce estimates of the reserves even when there are negative values. However, many methods can break down in the presence of enough [in number and/or size] negative incremental claims if certain constraints are not met. Historically the chain-ladder method has been used as a gold standard [benchmark], due to its generalized use and ease of application. A method that improves on the gold standard is one that can handle situations where there are many negative incremental claims and/or some of these are large. This paper presents a Bayesian model to consider negative incremental values, based on a three parameter log-normal distribution. The model presented here allows the actuary to provide point estimates and measures of dispersion, as well as the complete distribution for outstanding claims from which the reserves can be derived. The model applies Markov Chain Monte Carlo [MCMC] using the package WinBUGS.

Description: Using data from the Health & Retirement Study [HRS], a two-part medical claim prediction model is estimated for a cohort of survey respondents approaching Medicare-eligibility age. A High Deductible Health Plan [HDHP] with a companion Health Savings Account [HSA] is applied to simulated claims streams to model the build-up of HSA assets over the near-retirement years. Results show that the HSA is a grossly inadequate savings vehicle to provide for retiree medical care expenses at age 65. Moreover, HSA adequacy worsens exponentially with diminishing health status. Based on this simulation, it is apparent that Baby Boomers cannot adequately provide for the costs of medical care in retirement using HSAs exclusively.

Description: Automobile insurers classify the risks that they underwrite in order to subdivide the portfolio into classes of risks with similar profiles. While some insurers may have sufficient historical data, several others may not have significant volume of experience data in order to produce reliable claims predictions to help enhance their risk classification systems. A database containing a pooled experience of several insurers thereby helps to produce a more fair, reliable, and equitable premium structure for all risks concerned. This paper uses multilevel models to analyze the data on claim counts provided by the General Insurance Association of Singapore, an organization consisting of most of the general insurers in Singapore. The multilevel nature of the data is due to the following: a certain vehicle is observed over a period of years and is insured by a particular insurance company under a certain 'fleet' policy. The authors show how intercompany data lead to a priori premiums and a posteriori corrections to these initial premiums. Specific focus is made in understanding the intercompany effects using various count distribution models [Poisson, negative binomial, zero–inflated and hurdle Poisson]. The performance of these various models is compared the authors also investigate how to use the historical claims of a company, fleet and/or vehicle in order to correct for the premium initially set.

Description: Premium computation in a Bayesian context requires the use of a prior distribution [structure function] that the risk parameter follows in the heterogeneous portfolio. This paper contributes to the analysis of credibility theory by identifying the unique relationship between the prior distribution and credibility formula. The latter corresponds to a suggestive form of expressing the premium to be charged to a policyholder as a weighted sum of the sample mean and collective premium. Results for net premium principle and Poisson and negative binomial likelihood functions are shown.

Description: Recent articles addressed the subject of fuzzy regression [FR] and the term structure of interest rates [TSIR]. Their approach relied on possibilistic regression. Although possibilistic regression has been used in many applications, it has a number of limitations, not the least of which is its nebulous relation to the least-squares concept. As an alternative to possibilistic regression, this paper uses fuzzy least square regression to investigate the TSIR.

Description: This presentation develops a micro–level stochastic model for the run–off of automobile insurance claims. The analysis uses policy exposure, claims and payments experience data from vehicle insurance portfolios obtained from a major general insurance company in Singapore. The data are from the General Insurance Association 'GIA' of Singapore, an organization comprising most of the general insurers in Singapore. Modelling the run–off of individual Reported But Not Settled [RBNS] claims is the very aim of the work. The presenters focus on the following components of the development process: the time to an event, the conditional event type, the conditional payment type if any, and the conditional severity if any. They distinguish three types of events: settlement without any payments made during development, settlement with a payment and a payment without settlement. Given that a payment is to be made, the conditional payment type model describes the probability that it will be one of three claim types, or any possible combination of them. The conditional severity component describes the claim amount structure according to the combination of types paid. The presenters provide appropriate statistical models for each component and calibrate them to the available data. These building blocks are consequently used to predict the future development of open RBNS claims.

Description: Many quantities arising in non-life insurance depend on claim severity distributions, which are usually modeled assuming a parametric form. Obtaining good estimates of the quantities, therefore, reduces to having good estimates of the model parameters. However, the notion of 'good estimate' depends on the problem at hand. For example, the maximum likelihood estimators [MLE] are efficient, but they generally lack robustness. Since outliers are common in insurance loss data, it is therefore important to have a method that allows one to balance between efficiency and robustness. This presentation suggests a general estimation method that we call the method of trimmed moments [MTM]. This method is appropriate for various model fitting situations including those for which a close fit in one or both tails of the distribution is not required. The MTM estimators can achieve various degrees of robustness, and they also allow the decision maker to easily see the actions of the estimators on the data, which makes them particularly appealing.

Description: The insurance industry is known to have high operating expenses in the financial services sector. Insurers, investors and regulators are interested in models to understand the behavior of expenses. However, the current practice ignores skewness, occasional negative values as well as their temporal dependence. Addressing these three features, this presentation develops a longitudinal model of insurance company expenses that can be used for prediction, to identify unusual behavior, and to measure firm efficiency. Specifically, it uses a three parameter asymmetric Laplace density for the marginal distribution of insurers’ expenses in each year. Copula functions are employed to accommodate their temporal dependence. As a function of explanatory variables, the location parameter allows the presenters to analyze an insurer’s expenses in light of the firm’s characteristics. Their model can be interpreted as a longitudinal quantile regression.

Description: This abstract describes a paper that discusses insurance claim forecasting using econometric stepwise regression to analyze historical data.

Description: Because of the growing significance of Enterprise Risk Management, it is critical to consider how ERM responds and relates to circumstances and conditions. In particular, one megatrend currently impacting our world and our understanding of the economy is the emergence of a behavioral economics perspective. This paper describes the nature of behavioral economics, and considers the potential impact of such a perspective on ERM. From Actuarial Research Clearing House, 2012, Vol. 1.