A unified approach to generate risk measures

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Author's Abstract

The paper derives many existing risk measures and premium principles by minimizing a Markov bound for the tail probability. Our approach involves two exogenous functions ν(S) and φ(S, π) and another exogenous parameter α ยท 1. Minimizing a general Markov bound leads to the following unifying equation:

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For any random variable, the risk measure π is the solution to the unifying equation. By varying the functions φ and ν, the paper derives the mean value principle, the zeroutility premium principle, the Swiss premium principle, Tail VaR, Yaari's dual theory of risk, mixture of Esscher principles and more. The paper also discusses combining two risks with super-additive properties and sub-additive properties. In addition, we recall some of the important characterization theorems of these risk measures.

Resource: [1] Title: A unifed approach to generate risk measures Authors: Marc J. Goovaerts, Rob Kaasb, Jan Dhaene, Qihe Tang

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