Year: 2003
Type: article
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 φ(S, π) and another exogenous parameter α ≤ 1. Minimizing a general Markov bound leads to the following unifying equation: E [φ (S, π)] = αE [v (S)]. For any random variable, the risk measure π is the solution to the unifying equation. By varying the functions φ 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.
Source: Astin Bulletin
Authors: Marc J. Goovaerts, Rob Kaas, Jan Dhaene, Qihe Tang
Institutions: KU Leuven, University of Amsterdam
Language: English
Topic: Probability and Risk Models
Field: Decision Sciences
Domain: Social Sciences
Open Access status: bronze
OpenAlex ID: W2103187733