Towards a topological representation of risks and their measures

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number134
JournalRisks
Volume6
Issue number4
DOIs
StatePublished - 1 Dec 2018

Keywords

  • Diversification
  • Portfolio theory
  • Risk measurement
  • Risk measures
  • Set-valued measures
  • Topological spaces
  • Topology

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