Set-valued average value at risk and its computation
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New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first ’regulator’ version is independent from any market model whereas the second version, called the market extension, takes trading opportunities into account. Essential properties of both versions are proven and an algorithmic approach is provided which admits to compute the values of both versions over finite probability spaces. Several examples illustrate various features of the theoretical constructions.
KeywordsAverage value at risk Set-valued risk measures Coherent risk measures Transaction costs Benson’s algorithm
Mathematics Subject Classification (2000)91B30 46N10 26E25 46A20
JEL ClassificationsC61 G32
The authors emphasize that this project benefited from discussions with Frank Heyde (about the primal definition of AV@R) and Andreas Löhne (about the computational part). We are grateful to the referees of a previous version for their constructive remarks. Birgit Rudloff’s research was supported by NSF award DMS-1007938.
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