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Expectile Quadrangle and Applications

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  • Viktor Kuzmenko
  • Anton Malandii
  • Stan Uryasev

Abstract

The paper explores the concept of the \emph{expectile risk measure} within the framework of the Fundamental Risk Quadrangle (FRQ) theory. According to the FRQ theory, a quadrangle comprises four stochastic functions associated with a random variable: ``error'', ``regret'', ``risk'', and ``deviation''. These functions are interconnected through a stochastic function known as the ``statistic''. Expectile is a risk measure that, similar to VaR (quantile) and CVaR (superquantile), can be employed in risk management. While quadrangles based on VaR and CVaR statistics are well-established and widely used, the paper focuses on the recently proposed quadrangles based on expectile. The aim of this paper is to rigorously examine the properties of these Expectile Quadrangles, with particular emphasis on a quadrangle that encompasses expectile as both a statistic and a measure of risk.

Suggested Citation

  • Viktor Kuzmenko & Anton Malandii & Stan Uryasev, 2023. "Expectile Quadrangle and Applications," Papers 2306.16351, arXiv.org, revised Jul 2023.
    • Handle: RePEc:arx:papers:2306.16351
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    File URL: http://arxiv.org/pdf/2306.16351
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