Résumé
In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the risks taken by financial institutions, such as banks and insurance companies, acceptable to the regulator. In recent years attention has turned towards convex and coherent risk measurement. A risk measure is defined as a mapping from a set of random variables to the real numbers. This set of random variables represents portfolio returns. The common notation for a risk measure associated with a random variable is . A risk measure should have certain properties: Normalized Translative Monotone In a situation with -valued portfolios such that risk can be measured in of the assets, then a set of portfolios is the proper way to depict risk. Set-valued risk measures are useful for markets with transaction costs. A set-valued risk measure is a function , where is a -dimensional Lp space, , and where is a constant solvency cone and is the set of portfolios of the reference assets. must have the following properties: Normalized Translative in M Monotone Value at risk Expected shortfall Superposed risk measures Entropic value at risk Drawdown Tail conditional expectation Entropic risk measure Superhedging price Expectile Variance (or standard deviation) is not a risk measure in the above sense. This can be seen since it has neither the translation property nor monotonicity. That is, for all , and a simple counterexample for monotonicity can be found. The standard deviation is a deviation risk measure. To avoid any confusion, note that deviation risk measures, such as variance and standard deviation are sometimes called risk measures in different fields. There is a one-to-one correspondence between an acceptance set and a corresponding risk measure. As defined below it can be shown that and . If is a (scalar) risk measure then is an acceptance set. If is a set-valued risk measure then is an acceptance set.
À propos de ce résultat
Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.
Cours associés (2)
FIN-417: Quantitative risk management
This course is an introduction to quantitative risk management that covers standard statistical methods, multivariate risk factor models, non-linear dependence structures (copula models), as well as p
MGT-302: Data driven business analytics
This course focuses on on methods and algorithms needed to apply machine learning with an emphasis on applications in business analytics.
Publications associées (33)