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Risks 2018, 6(4), 134; https://doi.org/10.3390/risks6040134

Towards a Topological Representation of Risks and Their Measures

Department of Business Administration, Guilford Glazer Faculty of Business and Management, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 8410501, Israel
Received: 8 October 2018 / Revised: 9 November 2018 / Accepted: 15 November 2018 / Published: 19 November 2018
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Abstract

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. View Full-Text
Keywords: diversification; portfolio theory; risk measurement; risk measures; set-valued measures; topology; topological spaces diversification; portfolio theory; risk measurement; risk measures; set-valued measures; topology; topological spaces
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Shushi, T. Towards a Topological Representation of Risks and Their Measures. Risks 2018, 6, 134.

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