Mathematics and Financial Economics

, Volume 7, Issue 2, pp 229-246

First online:

Set-valued average value at risk and its computation

  • Andreas H. HamelAffiliated withDepartment of Mathematical Sciences, Yeshiva University
  • , Birgit RudloffAffiliated withORFE, BCF, Princeton University Email author 
  • , Mihaela YankovaAffiliated withBarclays Capital

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.


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

Mathematics Subject Classification (2000)

91B30 46N10 26E25 46A20

JEL Classifications

C61 G32