Interpolis (Netherlands)

The effects of vulnerability, severity, costs, effort, and effectiveness on prevention behavior, derived from protection motivation theory and the health belief model, have been extensively tested in the literature and have all been shown to predict rather well. In this study we test the effects of these determinants in a new context: the domestic risk prevention domain. The specific behaviors under study are related to the risks of burglary, fire, and water damage. In addition to previous studies, our multilevel research design allows us to evaluate which differences in the performance of domestic prevention behavior can be attributed to differences between persons and which to differences between behaviors within persons. Our results show that all determinants are relevant predictors for domestic risk prevention behavior. Disentangling the within‐person and between‐person effects shows that prevention behavior depends more on the relative evaluation of the prevention behavior determinants for a given person (e.g., a person perceives a smoke alarm to be more effective than antiburglar strips), than on the differences between persons regarding the general perception of these determinants (e.g., some persons find prevention behaviors in general more effective than other persons). To increase the performance of domestic risk prevention behaviors, we advise that interventions should focus on increasing a person's perception of risks and prevention behaviors relative to other risks and prevention behaviors rather than focusing on changing people's general perceptions of all risks and behaviors or focusing on specific target groups.

The calculation of mean claim sizes, in the presence of a deductible, is usually achieved through numerical integration. In case of a Lognormal or Gamma distribution, the quantities of interest can easily be expressed as functions of the cumulative distribution function, with modified parameters. This also applies to the F-distribution, where the incomplete Beta function enters the scene; see for instance the appendix in Hogg and Klugman (1984).The purpose of this paper is to derive an explicit formula for the first two moments of the Inverse Gaussian distribution, in the presence of censoring. For reasons of completeness we also consider truncation of the Inverse Gaussian distribution by an upper limit.The tractability of the derivation depends in a crucial way on two properties of the Inverse Gaussian distribution. Firstly, the cumulative distribution function of the Inverse Gaussian can be written as a simple function using the Normal probability integral. Secondly, the moment generating function of a censorized Inverse Gaussian distribution boils down to an expression containing the cumulative Inverse Gaussian distribution. This manifests itself most clearly in case of life insurance where the quantity of interest is the expectation of a present value. In case of non-life insurance, where the dimension of the Inverse Gaussian random variable is money instead of time, a further step is required: differentiation of the moment generating function.So, a natural order of this paper is to address ourselves first to the derivation for the life case and afterwards tackling the more laborious derivation for the non-life case.