Risk minimization and set-valued average value at risk via linear vector optimization

Details Risk minimization and set-valued average value at risk via linear vector optimization Risk minimization and set-valued average value at risk via linear vector optimization

2012-02-25

arxiv.org/abs/1202.5702v1

Economy

Quantitative Finance

Risk Management

Scientific paper

In this paper, the market extension of set-valued risk measures for models with proportional transaction costs is linked with set-valued risk minimization problems. As a particular example, the set-valued average value at risk (AV@R) is defined and its market extension and corresponding risk minimization problems are studied. We show that for a finite probability space the calculation of the values of AV@R reduces to linear vector optimization problems which can be solved using known algorithms. The formulation of AV@R as a linear vector optimization problem is an extension of the corresponding scalar result by Rockafellar and Uryasev.

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