Towards a Topological Representation of Risks and Their Measures
In risk theory, risks are often modeled by risk measures which allow quantifying the risks and estimating their possible outcomes. Risk measures rely on measure theory, where the risks are assumed to be random variables with some distribution function. In this work, we derive a novel topological-bas...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-11-01
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| Series: | Risks |
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| Online Access: | https://www.mdpi.com/2227-9091/6/4/134 |
| _version_ | 1818274837993357312 |
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| author | Tomer Shushi |
| author_facet | Tomer Shushi |
| author_sort | Tomer Shushi |
| collection | DOAJ |
| description | In risk theory, risks are often modeled by risk measures which allow quantifying the risks and estimating their possible outcomes. Risk measures rely on measure theory, where the risks are assumed to be random variables with some distribution function. In this work, we derive a novel topological-based representation of risks. Using this representation, we show the differences between diversifiable and non-diversifiable. We show that topological risks should be modeled using two quantities, the risk measure that quantifies the predicted amount of risk, and a distance metric which quantifies the uncertainty of the risk. |
| first_indexed | 2024-12-12T22:20:13Z |
| format | Article |
| id | doaj.art-e90aaa6f903a434296967bd8e99db4dc |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-12-12T22:20:13Z |
| publishDate | 2018-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-e90aaa6f903a434296967bd8e99db4dc2022-12-22T00:09:57ZengMDPI AGRisks2227-90912018-11-016413410.3390/risks6040134risks6040134Towards a Topological Representation of Risks and Their MeasuresTomer Shushi0Department of Business Administration, Guilford Glazer Faculty of Business and Management, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 8410501, IsraelIn risk theory, risks are often modeled by risk measures which allow quantifying the risks and estimating their possible outcomes. Risk measures rely on measure theory, where the risks are assumed to be random variables with some distribution function. In this work, we derive a novel topological-based representation of risks. Using this representation, we show the differences between diversifiable and non-diversifiable. We show that topological risks should be modeled using two quantities, the risk measure that quantifies the predicted amount of risk, and a distance metric which quantifies the uncertainty of the risk.https://www.mdpi.com/2227-9091/6/4/134diversificationportfolio theoryrisk measurementrisk measuresset-valued measurestopologytopological spaces |
| spellingShingle | Tomer Shushi Towards a Topological Representation of Risks and Their Measures Risks diversification portfolio theory risk measurement risk measures set-valued measures topology topological spaces |
| title | Towards a Topological Representation of Risks and Their Measures |
| title_full | Towards a Topological Representation of Risks and Their Measures |
| title_fullStr | Towards a Topological Representation of Risks and Their Measures |
| title_full_unstemmed | Towards a Topological Representation of Risks and Their Measures |
| title_short | Towards a Topological Representation of Risks and Their Measures |
| title_sort | towards a topological representation of risks and their measures |
| topic | diversification portfolio theory risk measurement risk measures set-valued measures topology topological spaces |
| url | https://www.mdpi.com/2227-9091/6/4/134 |
| work_keys_str_mv | AT tomershushi towardsatopologicalrepresentationofrisksandtheirmeasures |