Miller N, Ruszczynski A (2008) Risk-adjusted probability measures in portfolio optimization with coherent measures of risk. Eur J Oper Res 191:193–206Miller, N., & Ruszczyński, A. (2008). Risk-adjusted probability measures in portfolio optimization with coherent measure of risk. European ...
Inthepaper“CoherentmeasuresofRisk”(,July1999)asetofaxiomswasproposedasthekeypropertiestobesatisfiedbyany“coherentmeasureofrisk”.ThediversificationprinciplegoeshereValueatRisk(VaR):howitworksTocomputeVaR,weneedtospecifyAtimehorizon:Aconfidencelevel:forinstancea5%.ThedefinitionofVaRisthen:“TheVaRofaportfolio...
(intime)?howeverabsolutelygeneral Part1:DefiningaRiskMeasure Thequalitativeconceptof“risk”and“riskpremium”Everybodyhasaninnatefeelingforfinancialrisk...moreorlessthis...Howtodefineriskinaquantitativefashion?...ConceptofRisk ?RiskMeasure fundamentalshared principles test requirements(axioms)onthe ...
sets. We argue that these axioms should hold for any risk measure that is to be used to effectively regulate or manage risks. We call risk measures that satisfy the four axioms coherent. (4) In Section 3, we present a (simplified) description of three existing methods for measuring mark...
基于上述风险测度的局限性,Artzner等(1999)提出了一致性风险测度(Coherent Risk Measure)概念。他们认为一种良好定义的风险测度应该满足单调性、正齐次性、平移不变性和次可加性四条公理,并将满足这些公理的风险测度成为一致性风险测度。定义ρ(X)为风险测度,X为资产x的损失金额,X是一个随机变量。
5) coherent measure of risk 一致性风险度量 1. The CVaR model,which was based oncoherent measure of risk,lacks of dynamic properties for multi-period risk measures,especially dynamic consistency. 基于一致性风险度量公理建立的CVaR方法缺乏多时期风险度量属性,特别是动态持续性。
4) Coherent Risk Measure 一致风险测度 1. In this paper we take the investment target into the risk definition,and propose a new axiomatic framework for the class of generalized coherent risk measures. 将资产的目标价值以直观的方式加入到风险的定义中,提出了广义一致风险测度公理假设,并证明了广义...
A spectral risk measure (SRM) is arisk measurethat is calculated as a weighted average of outcomes, the weights of which depend on the user's risk aversion. Unlike value at risk (VaR), for example, it is an example of a 'coherent risk measure' as described in the field of mathematical...
The general dual representation for convex and coherent risk measures is given in Section 4. Various examples are provided in Section 5. In many situations, it is reasonable to assume that a risk measure depends on the randomness of the portfolio value only through its probability law. Such ...
Again, a risk-neutral measure Q refers to the normalized version of a linear price system in the sense of Arrow–Debreu. However, under volatility uncertainty, priors in P can be mutually singular. On the one hand, linear and positive prices only capture strictly positive payoffs in events ...