Individual Risk Theory and Risk Statistics as Applied to Fire Insurance

Abstract

Risk Theory for Life Insurance is simplified by the fact that the distribution Ψ (x) of claim amounts x approximately coincides with the distribution of “Risk sums” (not exactly, owing to differaences in the claim frequency with age and actual state of health), ond this distribution is comparatively stable.—The dependence on the claim frequency is eliminated by the introduction of a new time variable, and the system reduced to a (stationary) Poisson Process, which should be valid at least for large risk systems and for the total Life branch for a moderate sequence of years.In almost all non-life branches, partial claims will dominate and Ψ (x) can only be determined by risk statistics, leaving a certain space of indetermination, in particular for large claims and for mediumsized statistical risk groups.In my previous analyses, in particular New York 1957, interest has been concentrated on traffic and motor car insurance, where the risk depends on cars insured and on the meeting traffic (including road conditions). In one year the same car can be involved in many accidents and double claims (=collisions) are rather frequent.—According to my experience, this system is best represented by a sequence of single and double risk situations in time (for individual cars or for risk groups).Analysis is simplified for Fire Insurance (and many other non-life branches), because the risk system is composed of mostly independent insurances (or risk objects), which are best described by the ordinary Individual Risk Theory.