Empirical Investigation of Insurance Claim Dependencies Using Mixture Models

Download or read book Empirical Investigation of Insurance Claim Dependencies Using Mixture Models written by Emiliano A. Valdez and published by . This book was released on 2013 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: For several years now, there continues to be attention in the modeling of insurance and other similar type of risks, such as the risk of credit default, to incorporate the presence of dependencies. Some of the early papers appearing in the literature demonstrate that for a typical portfolio of such risks, ignoring dependencies can have a direct impact on the tail or extremes of the resulting portfolio loss distribution. The tail of the loss distribution is something not to be ignored by the actuary or the risk manager. To date, in spite of this growing number of papers in the literature on dependence modeling, we find that there is no known published work that provides for an empirical evidence to validate the presence of dependencies in an insurance portfolio. In this paper, we use mixture models, customarily suggested to model dependent credit default risks, to facilitate the investigation of claim dependencies. The empirical data used to calibrate these models came from a portfolio of automobile insurance policies drawn from a randomly selected insurance provider. In order to measure the presence of claim dependencies, one of the most reasonable statistic to use is the relative risk ratio, a measure that is widely popular in medical statistics and is used to gauge how the claim occurrence of a particular insurance risk induces claim of another insurance risk. Our calibration results indicate some presence of positive dependencies; relative risk is in the neighborhood of 1.4 and resulting pair-wise correlation is 0.04. The model naturally extends to capture policyholder heterogeneity through the presence of co-variates by introducing mixture models with co-variates as explained in this article. Not surprisingly, because the premium is the actuary's best guess of the degree of riskiness of an insurance risk, at least on an a priori basis, it provides for the single most important factor that influences the presence of claim dependencies.