Non-Cash Risk Measure on Nonconvex Sets
Monetary risk measures defined on a convex set are interpreted as the smallest amount of external cash that must be added to a portfolio to make the portfolio being acceptable. In the present paper, the authors introduce a new concept: non-cash risk measure, which does as a nonconvex risk measure wo...
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| Format: | Article |
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MDPI AG
2018-10-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/6/10/186 |
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doaj-c63c5d241d974999823bb216f24caadc2020-11-24T21:28:03ZengMDPI AGMathematics2227-73902018-10-0161018610.3390/math6100186math6100186Non-Cash Risk Measure on Nonconvex SetsChang Cong0Peibiao Zhao1School of Science, Nanjing University of Science and Technology, Nanjing 210094, ChinaSchool of Science, Nanjing University of Science and Technology, Nanjing 210094, ChinaMonetary risk measures defined on a convex set are interpreted as the smallest amount of external cash that must be added to a portfolio to make the portfolio being acceptable. In the present paper, the authors introduce a new concept: non-cash risk measure, which does as a nonconvex risk measure work in a nonconvex set. In addition, the authors arrive at a convex extension of the non-cash risk measure, and offer the relationship between the non-cash risk measure and its extension.http://www.mdpi.com/2227-7390/6/10/186risk measuresnon-cash measurenonconvex setsnonconvex measures |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Chang Cong Peibiao Zhao |
| spellingShingle |
Chang Cong Peibiao Zhao Non-Cash Risk Measure on Nonconvex Sets Mathematics risk measures non-cash measure nonconvex sets nonconvex measures |
| author_facet |
Chang Cong Peibiao Zhao |
| author_sort |
Chang Cong |
| title |
Non-Cash Risk Measure on Nonconvex Sets |
| title_short |
Non-Cash Risk Measure on Nonconvex Sets |
| title_full |
Non-Cash Risk Measure on Nonconvex Sets |
| title_fullStr |
Non-Cash Risk Measure on Nonconvex Sets |
| title_full_unstemmed |
Non-Cash Risk Measure on Nonconvex Sets |
| title_sort |
non-cash risk measure on nonconvex sets |
| publisher |
MDPI AG |
| series |
Mathematics |
| issn |
2227-7390 |
| publishDate |
2018-10-01 |
| description |
Monetary risk measures defined on a convex set are interpreted as the smallest amount of external cash that must be added to a portfolio to make the portfolio being acceptable. In the present paper, the authors introduce a new concept: non-cash risk measure, which does as a nonconvex risk measure work in a nonconvex set. In addition, the authors arrive at a convex extension of the non-cash risk measure, and offer the relationship between the non-cash risk measure and its extension. |
| topic |
risk measures non-cash measure nonconvex sets nonconvex measures |
| url |
http://www.mdpi.com/2227-7390/6/10/186 |
| work_keys_str_mv |
AT changcong noncashriskmeasureonnonconvexsets AT peibiaozhao noncashriskmeasureonnonconvexsets |
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1725971802432208896 |