A Model for Policy-Size and Diversification Discounts

By Jay Michael Call

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Abstract

An actuarial approach for calculating a relativity based on geographic diversification is presented. The method models correlation as a function of distance between two exposures, and uses that to calculate a risk margin for each policy. It assumes that any premium provision for a company risk margin is currently allocated in proportion to policy risk-free premium, which results in a uniform risk-loading uprate for all policies. It is suggested that a better approach would be to allocate com-pany risk margin in proportion to policy risk margin so that more diverse policies incur a smaller risk factor. This approach results in a range of diversification relativities that tends to be very narrow, so a revenue-neutral method for magnifying the impact of the diversification relativity is also presented. Approaches for reflecting non-geographic forms of diversification (such as for package policies) are also discussed. And, since policies with many insured items have a greater potential for diversity than policies with fewer insured items, the diversification relativities presented herein could also be viewed as a type of policy-size relativity.

Keywords Diversification relativity, risk-free premium, risk margin, risk factor, coefficient of variation, book diversification ratio, geographic diversification, distance-correlation model, geocode, distance formula

Citation

Call, Jay Michael, "A Model for Policy-Size and Diversification Discounts," Variance 13:1, 2020, pp. 93-123.

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Mission Statement

Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.