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Document Details : Title: A Unified Approach to Generate Risk Measures Author(s): GOOVAERTS, Marc J. , KAAS, Rob , DHAENE, Jan , TANG, Qihe Journal: ASTIN Bulletin Volume: 33    Issue: 2   Date: November 2003    Pages: 173-191 DOI: 10.2143/AST.33.2.503689 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 v(S) and f(S, p) and another exogenous parameter a¡Ü1. Minimizing a general Markov bound leads to the following unifying equation: E[f(S. p)] = aE[v(S)] For any random variable, the risk measure p is the solution to the unifying equation. By varying the functions f and v, the paper derives the mean value principle, the zero-utility 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.