Property Damage Liability Research Articles

Estimating the Total Claims Distribution Using Multivariate Frequency and Severity Distributions

Traditionally, the random variable total annual losses has been treated as if it were generated by univariate frequency and severity processes. This approach either reflects the explicit assumption that only a single loss process is present or represents the aggregation of losses from multiple sources as in collective risk theory. This article presents a model that utilizes multivariate frequency and severity distributions to analyze total annual losses when multiple loss processes are present. Unlike the traditional approach, the multivariate technique allows explicit recognition of dependencies among the components of the overall process. Multivariate frequency and severity distributions that might be appropriate in insurance and risk management applications are discussed. Finally, the model is applied using the bodily injury and property damage liability claims experience of two fleets of vehicles. The central problem in risk theory is modeling the probability distribution of total claims. The total claims distribution and its components, the frequency and severity distributions, then are used to evaluate reinsurance and deductible programs, to compute ruin probabilities, and to provide other information of interest to decision makers. For most organizations, total claims arise from exposure to multiple perils, each of which typically can produce more than one type of claim. The most general case involves a three-stage process: a multivariate accident process where each accident can lead to multivariate claims frequency and severity processes. Statistical dependencies could be present at a number of points, but the authors consider the following the most important: (1) dependencies among the accident frequency processes, (2) dependencies among claims frequencies of the same or different types for a given accident type, and (3) dependencies among severities arising out of a given accident of a particular type. For example, weather conditions could affect the frequency of both fires and automobile accidents. Ignoring such dependencies can lead to serious underestimates in J. David Cummins is the Harry J. Loman Professor of Property-Liability Insurance at the Wharton School of the University of Pennsylvania. He has a Ph.D. from the same institution. He is Associate Director of the S. S. Huebner Foundation for Insurance Education, an academic member of the ARIA Board of Directors, and a Past Chairman of the ARIA Risk Theory Seminar. He is the author or co-author of numerous books and professional journal articles. Laurel J. Wiltbank is an Instructor in Economics at Colgate University. She holds a Ph.D. degree from the University of Pennsylvania and is a member of the ARIA Risk Theory Seminar.

The Market Performance of Diversified and Non-Diversified Organizations within the P-L Insurance Industry

The Market Performance of Diversified and Non-Diversified Organizations within the P-L Insurance Industry

Public Desires and Automobile Property Damage Insurance

In an article in this issue of the Journal, the authors conclude that sufficient evidence does not exist to warrant the modification or abolition of the negligence concept as it applies to automobile property damage.' In an effort to provide further information pertaining to the question whether the automobile property damage liability insurance system should be changed, a questionnaire was developed to investigate consumer desires. Although many questionnaires pertaining to automobile insurance have been reported in the literature, none has focused upon automobile property damage insurance. Such is the objective of this research. The justification is that any changes in the system for compensating automobile property damage losses should not be made without consideration of the desires of the public. This study includes a random sample of 300 households whose automobiles had been involved in accidents in South Carolina during 1972-73. The names of the households were obtained from a major state agency. Persons from these households were selected for interview because it was believed that they would have a realistic basis upon which to judge the need for, and suggest changes in the present automobile insurance system. From the 300 households selected, a response rate of 80 percent was obtained through telephone interviews and 240 questionnaires were completed during October and November 1973.2 Respondents were in-

Should the "No-Fault" Concept Be Applied to Automobile Property Damage?

In this study the automobile bodily injury liability insurance claims settlement process is compared to that of the property damage liability insurance system. The objective is to determine if similar problems exist in both settlement processes such that legislative modifications of both systems are warranted. In addition, the claims settlement process under automobile medical payments insurance and collision insurance are compared to their corresponding liability insurance coverages to provide an improved perspective of the claims settlement process. These analyses do not suggest either that modification or abandonment of negligence law in its application to property damage claims is warranted. Summary conclusions are that substantial differences exist between the settlement of property damage liability insurance claims and bodily injury liability insurance claims. Only minor differences were found in the settlement of first party collision insurance claims and property damage liability insurance claims. Indications are that the benefits to be derived from the preservation of the property damage tort liability insurance system outweigh any potential benefits to be gained by its elimination.