Abstract:
This paper deals with multidimensional coherent and convex risk measures. The approach described takes into account risks of changing currency exchange rates and transaction costs. Representation theorems for multidimensional risk measures are proved. The important examples of multidimensional coherent risk measures such as tail V@R and weighted V@R are investigated. Two applications of multidimensional coherent risk measures are considered, i.e., application to the capital allocation problem and to the problem of risk contribution.
Keywords:multidimensional coherent and convex risk measures, matrix of currency exchange rates, cone of currency exchange rates, tail V@R, weighted V@R, capital allocation, risk contribution, extreme elements.
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