Eliciting claims development patterns and costs hidden in backlogs

We reconsider the problem of producing fair and accurate tariffs based on aggregated insurance data giving numbers of claims and total costs for the claims. Jørgensen and de Souza (Scand Actuarial J., 1994) assumed Poisson arrival of claims and gamma distributed costs for individual claims. Jørgensen and de Souza (1994) directly modelled the risk or expected cost of claims per insured unit,μsay. They observed that the dependence of the likelihood function onμis as for a linear exponential family, so that modelling similar to that of generalized linear models is possible. In this paper we observe that, when modelling the cost of insurance claims, it is generally necessary to model the dispersion of the costs as well as their mean. In order to model the dispersion we use the framework of double generalized linear models. Modelling the dispersion increases the precision of the estimated tariffs. The use of double generalized linear models also allows us to handle the case where only the total cost of claims and not the number of claims has been recorded.

ObjectiveTo determine whether psychological distress associated with musculoskeletal injuries sustained in a motor vehicle crash (MVC), regardless of time of onset, impacts compensation outcomes such as claim settlement times and...

The original paper with this title was published in 1968, following presentation at a Casualty Actuarial Society meeting. This is another up-date of indexes in the economic model—first report of 1976 and a forecast for 1977. These LPI indexes measure economic factors affecting loss and loss adjustment settlement costs which are incurred after claims have been reported. The indexes measure direct claims costs and not the reinsured excess losses which would be more adversely affected by inflation.This is a Claims Market Place concept of the loss settlement function of the insurance company. Claims Costs (our economic cost of production) result from purchasing of services under unusual circumstances in controversial, severe, hasty and often emergency situations. Claims settlements can take place in court rooms, lawyers' offices, repair garages and hospitals. The legalistic atmosphere is often one of friction and excessive demand rather than of a normal commercial esprit de corps. The procurement of these claims services requires dealing with high cost furnishers of services: doctors, clinics, hospitals, lawyers, repair garages or body shops, building trades, house furnishings.

This paper investigates the H∞ containment control problem of multi-agent systems with random communication time-delay. The information exchanges between the agents are supposed to be randomly delayed, characterized by a Bernoulli distribution sequence. And a neighbor-based protocol with random communication delay is proposed. As external perturbation exits broadly in many practical systems, the paper deals with it by using H∞ control theory. By applying stochastic technique, Lyapunov analysis and the free-weighting matrices technique, theoretical results show that the followers will ultimately converge to the convex hull spanned by the leaders in the mean square sense with a prescribed H∞ performance index. Finally, a numerical example is given to demonstrate the validity of the theoretical results.

The analysis of individual risks in insurance raises problems that occur in any statistical analysis of longitudinal data. Considering insurance data, the endogeneous variables are severity variables (for instance: number and cost of claims, duration of compensations, and so on). The exogeneous variables of the current period can be first be used as rating factors in an a priori rating model. The allowance for the history of the policyholder in a rating model is more intricate, and it can be performed from two different approaches. They are related to interpretations of serial correlation for individual data that can be summarized in the following way.

This paper estimates an empirical model of the total costs of finalised workers' compensation claims. The sample was comprised of 8232 claims, made by workers in Western Australia, that were closed in 1990. It is reported that the variables representing the method of claim settlement is an important determinant of the cost of individual workers' compensation claims. In addition, it is also found that type of injury, gender, age, and occupational classification have significant effects on the model. Workers who, sustain musculoskeletal injuries, are male, and/or who are white collar workers incur significantly more costs. In addition to these effects, a positive linear relationship between age and costs was also observed. The empirical models, of the kind specified in this paper, may be capable of performing a useful prescriptive role in rehabilitation programs. Such models can enable "problematic" cases to be identified early in the claim process, so that they might be appropriately referred for intensive rehabilitation intervention.

Previously published epidemiologic studies of low back pain (LBP) have reported that the prevalence of low back disability has increased dramatically. These studies based their findings on either the number of disability claims filed, the disability duration, or both. This information was from countries other than the United States or from the US Social Security Disability Insurance data, with findings reported only to the early 1980s. More recent studies of US workers' compensation LBP claims reported a decrease in the incidence rate from the late 1980s to the mid-1990s. No studies have been found that report on the trends of disability duration for workers' compensation LBP claims. This study examined recent trends in the length of disability (LOD) for LBP claims and associated costs, using a large sample of claims from the privately insured US workers' compensation market. LOD and cost information were derived for injuries from 1988, 1990, 1992, 1994, and 1996. For each year, the distributions of LOD and cost were skewed, with the small percentage of claims that lasted more than one year (4.6%-8.8%, depending on the year) accounting for a large percentage of the total disability days (77.6%-90.1%) and cost (64.9%-84.7%). From 1988 to 1996, the average LOD decreased 60.9%, from 156 days to 61 days. The probability of being on disability for a long period of time has decreased over the years. Over the study period, the average cost of a claim decreased 41.4%, while the median cost increased 19.7%. The most influential change in the LOD and cost distributions was a reduction in expensive claims with a long disability duration. The evolution of LOD and cost is also detailed for different disability durations for the study period.

In this paper, we present a new family of bivariate mixed exponential regression models for taking into account the positive correlation between the cost of claims from motor third party liability bodily injury and property damage in a versatile manner. Furthermore, we demonstrate how maximum likelihood estimation of the model parameters can be achieved via a novel Expectation-Maximization algorithm. The implementation of two members of this family, namely the bivariate Pareto or, Exponential-Inverse Gamma, and bivariate Exponential-Inverse Gaussian regression models is illustrated by a real data application which involves fitting motor insurance data from a European motor insurance company.

Abstract. Hailstorms occur frequently in metropolitan Sydney, in the eastern Australian State of New South Wales, which is especially vulnerable due to its building exposure and geographical location. Hailstorms challenge disaster response agencies and pose a great risk for insurance companies. This study focuses on the Sydney hailstorm of 14 April 1999 – Australia's most expensive insured natural disaster, with supporting information from two other storms. Comparisons are drawn between observed hailstone sizes, radar-derived reflectivity and damage data in the form of insurance claims and emergency calls. The "emergency response intensity" (defined by the number of emergency calls as a proportion of the total number of dwellings in a Census Collection District) is a useful new measure of the storm intensity or severity experienced. The area defined by a radar reflectivity ≥55 dBZ appears to be a good approximation of the damage swath on ground. A preferred area for hail damage is located to the left side of storm paths and corresponds well with larger hailstone sizes. Merging hail cells appear to cause a substantially higher emergency response intensity, which also corresponds well to maximum hailstone sizes. A damage threshold could be identified for hailstone sizes around 2.5 cm (1 cm), based on the emergency response intensity (insurance claims). Emergency response intensity and claims costs both correlate positively with hailstone sizes. Higher claim costs also occurred in areas that experienced higher emergency response intensities.

When constructing parametric models to predict the cost of future claims, several important details have to be taken into account: (1) models should be designed to accommodate deductibles, policy limits, and coinsurance factors; (2) parameters should be estimated robustly to control the influence of outliers on model predictions; and (3) all point predictions should be augmented with estimates of their uncertainty. The methodology proposed in this article provides a framework for addressing all of these aspects simultaneously. Using payment per payment and payment per loss variables, we construct the adaptive version of method of winsorized moments (MWM) estimators for the parameters of truncated and censored lognormal distribution. Further, the asymptotic distributional properties of this approach are derived and compared with those of the maximum likelihood estimator (MLE) and method of trimmed moments (MTM) estimators, the latter being a primary competitor to MWM. Moreover, the theoretical results are validated with extensive simulation studies and risk measure robustness analysis. Finally, practical performance of these methods is illustrated using the well-studied dataset of 1500 U.S. indemnity losses.

Objective: Determine whether nonlinear analysis can identify breathing pattern trends that are indicative of the progression and outcome of acute lung injury (ALI). Methods: Male Sprague‐Dawley rats (n=10) received intratracheal instillation of either bleomycin (3–4 units/120–160μL PBS) or PBS (160μL). Baseline breathing was recorded in unanesthetized animals using whole‐body plethysmography every other day after surgery. Multiple epochs (600‐s) were selected and breath‐to‐breath variability of expiration (Te) was assessed systematically by linear (mean, coefficient of variation) and nonlinear (mutual information, sample entropy of intervals and successive differences) tools. At two weeks, lung collagen content was measured. Results: Linear analysis did not discriminate the severity or outcome of injury. In contrast, nonlinear methods showed a trend between decreased average entropy of successive differences of Te across time lags and acute injury. The increase in entropy of breath‐to‐breath magnitude changes of Te across time lags was significantly greater for the animals with fulminant injury compared to resolving injury. Lung collagen content was not different between groups. Conclusion: Nonlinear analysis identified subtle changes in breathing variability, indistinguishable by linear analysis, that correlate to injury acuity prior to development of fibrosis (HL080138, VA Research Service & T35 NHLBI Summer Research Program).

Liability concerns in contraceptive research and development

ABSTRACTObjective: Lane changes, which frequently occur when vehicles travel on major roads, may contribute to critical situations that significantly affect the traffic flow and traffic safety. Thus, knowledge of lane change situations is important for infrastructure improvements as well as for driver support systems and automated driving development projects. The objectives of this study were to evaluate the crash avoidance performance of a lane change driver support system, the Blind Spot Information System (BLIS) in Volvo car models, and to describe the characteristics of lane change crashes by analyzing detailed information from insurance claim reports.Methods: An overall evaluation of the safety effect of BLIS was performed by analyzing crash rate differences in lane change situations for cars with and without the optionally mounted BLIS system based on a population of 380,000 insured vehicle years. Further, crashes in which the repair cost of the host vehicle exceeded approximately US$1,250 were selected and compared. Finally, the study examined different precrash factors and crash configurations, using in-depth insurance claims data from representative lane change crash cases including all severity levels in a population of more than 200,000 insured vehicle years.Results: The technology did not significantly reduce the overall number of crashes when all types of lane change crashes and severity levels were considered, though a significant crash-reducing effect of 31% for BLIS cars was found when more severe crashes with a repair cost exceeding US$1,250 were analysed. Cars with the BLIS technology also have a 30% lower claim cost on average for reported lane change crashes, indicating reduced crash severity. When stratifying the data into specific situations, by collecting precrash information in a case-by-case study, the influence of BLIS was indicated to differ for the evaluated situations, although no significant results were found. For example, during general lane change maneuvers (i.e., not while exiting or entering highways or during weaving/merging situations) the crash rate was reduced by 14%, whereas in weaving/merging situations the crash rate increased.Conclusions: The insurance data analyzed provided useful information about real-world lane change crash characteristics by covering collisions in all crash severities and thus revealed information beyond what is available in, for example, data sets of police-reported crashes. This will guide further development of driver support systems. For crashes with repair cost exceeding US$1,250, a significant crash reduction was found, although the technology did not significantly reduce the total number of lane change crashes. An average lower insurance claim cost for cars equipped with the BLIS technology also indicated that the technology contributes to reduced crash severity even if crashes were not totally avoided. Stratifying the data into different lane change crash situations gave indications of the condition-specific performance of the system, even if the results were not statistically significant at the 95% level.

A large scale study on the dependence of time lag of runoff on snow depth and stratigraphy was carried out in a watershed. The time lag in peak runoff was found to be increased by 1.5 - 4 h per I m increment in snow depth. Although the data were widely scattered, it was found that the time lag series converged in a line every year and that discrete layers in the snow cover composed in a warm winter, accelerated meltwater flow. Subtracting the time of propagation through a snowcover from the total time lag, the effect of size of a watershed on a delay in runoff was rearranged, as follows: where Tf is the time lag in min after discharge from a snow cover, A the area of a watershed in km2, Re the effective snowmelt in mm/hr. The time lag Tf increases only by 1.5 times when an area of a watershed is increased by a factor of ten.

A large scale study on the dependence of time lag of runoff on snow depth and stratigraphy was carried out in a watershed. The time lag in peak runoff was found to be increased by 1.5 - 4 h per I m increment in snow depth. Although the data were widely scattered, it was found that the time lag series converged in a line every year and that discrete layers in the snow cover composed in a warm winter, accelerated meltwater flow.Subtracting the time of propagation through a snowcover from the total time lag, the effect of size of a watershed on a delay in runoff was rearranged, as follows: where Tf is the time lag in min after discharge from a snow cover, A the area of a watershed in km2, Re the effective snowmelt in mm/hr. The time lag Tf increases only by 1.5 times when an area of a watershed is increased by a factor of ten.