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Insurance Ratemaking and a Gini Index
Author(s) -
Frees Edward W. Jed,
Meyers Glenn,
Cummings A. David
Publication year - 2014
Publication title -
journal of risk and insurance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.055
H-Index - 63
eISSN - 1539-6975
pISSN - 0022-4367
DOI - 10.1111/j.1539-6975.2012.01507.x
Subject(s) - skewness , economics , lorenz curve , index (typography) , econometrics , gini coefficient , actuarial science , inequality , mathematics , economic inequality , computer science , mathematical analysis , world wide web
Welfare economics uses Lorenz curves to display skewed income distributions and Gini indices to summarize the skewness. This article extends the Lorenz curve and Gini index by ordering insurance risks; the ordering variable is a risk‐based score relative to price, known as a relativity. The new relativity‐based measures can cope with adverse selection and quantify potential profit. Specifically, we show that the Gini index is proportional to a correlation between the relativity and an out‐of‐sample profit (price in excess of loss). A detailed example using homeowners insurance demonstrates the utility of these new measures.