Kulikov, A. V. Multidimensional coherent and convex risk measures. (English. Russian original) Zbl 1156.91399 Theory Probab. Appl. 52, No. 4, 614-635 (2008); translation from Teor. Veroyatn. Primen. 52, No. 4, 685-710 (2007). Summary: 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. Cited in 8 Documents MSC: 91B30 Risk theory, insurance (MSC2010) 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 PDFBibTeX XMLCite \textit{A. V. Kulikov}, Theory Probab. Appl. 52, No. 4, 614--635 (2008; Zbl 1156.91399); translation from Teor. Veroyatn. Primen. 52, No. 4, 685--710 (2007) Full Text: DOI