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Similar risks have similar prices: A useful and exact quantification

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  • Mildenhall, Stephen J.

Abstract

We introduce a straightforward algorithm to determine a range of prices for a new risk consistent with known pricing on one or more risks and the assumption prices are determined by a law invariant, coherent or convex risk measure. In many cases the algorithm produces bounds tight enough to be useful in practice. We illustrate the theory by applying it to evaluating portfolio-level pricing by line and pricing for high limits policies relative to low limits. We also show how the theory can test if prices for a set of risks are generated by a single risk measure and show the conditions for this to be true are very strict.

Suggested Citation

  • Mildenhall, Stephen J., 2022. "Similar risks have similar prices: A useful and exact quantification," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 203-210.
    • Handle: RePEc:eee:insuma:v:105:y:2022:i:c:p:203-210
    DOI: 10.1016/j.insmatheco.2022.04.006
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    Keywords

    Law invariant; Coherent risk measure; Convex risk measure; Distortion risk measure; Insurance pricing; Comonotonic;
    All these keywords.

    JEL classification:

    • G19 - Financial Economics - - General Financial Markets - - - Other

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