Premium Calculation: Why Standard Deviation Should be Replaced by Absolute Deviation

Dieter Denneberg

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Probability and Risk Models Insurance and Financial Risk Management Probability and Statistical Research

Abstract

Abstract Average absolute (instead of quadratic) deviation from median (instead of expectation) is better suited to determine the safety loading for insurance premiums than standard deviation: The corresponding premium functionals behave additive under the practically relevant risk sharing schemes between first insurer and reinsurer.

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1987The Dual Theory of Choice under Risk 1964Smoothing, Forecasting and Prediction of Discrete Time Series.1979An introduction to mathematical risk theory 1989Additive Representations of Preferences 1988Additive Representations of Preferences: A New Foundation of Decision Analysis

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2008Spectral risk measures and portfolio selection 2017Pessimistic portfolio allocation and Choquet expected utility 2016Gini-Type Measures of Risk and Variability: Gini Shortfall, Capital Allocations, and Heavy-Tailed Risks 2004Premium Principles 2005Optimal reinsurance under convex principles of premium calculation 2018Characterization, Robustness and Aggregation of Signed Choquet Integrals 2014Robustifying Convex Risk Measures for Linear Portfolios: A Nonparametric Approach 2021A Theory for Measures of Tail Risk

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