Set-valued average value at risk and its computation Authors Andreas H. Hamel Department of Mathematical Sciences Yeshiva University Birgit Rudloff ORFE, BCF Princeton University Mihaela Yankova Article

First Online: 23 January 2013 Received: 21 September 2012 Accepted: 07 January 2013 DOI :
10.1007/s11579-013-0094-9

Cite this article as: Hamel, A.H., Rudloff, B. & Yankova, M. Math Finan Econ (2013) 7: 229. doi:10.1007/s11579-013-0094-9
Abstract 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.

Keywords Average value at risk Set-valued risk measures Coherent risk measures Transaction costs Benson’s algorithm

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