Modified Expected Shortfall: a Coherent Risk Measure for Elliptical Family of Distributions

Deepak K. Jadhav and Ramanathan Thekke Variyam ()
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Deepak K. Jadhav: Savitribai Phule Pune University
Ramanathan Thekke Variyam: Savitribai Phule Pune University

Sankhya B: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 8, 234-256

Abstract: Abstract The ‘Modified Expected Shortfall’ is a risk measure proposed by Jadhav et al. (J. Risk 16, 69–83, 2013) is not a coherent risk measure in general. In this paper, we prove that ‘Modified Expected Shortfall’ is a coherent risk measure under univariate and multivariate elliptical families of distributions. The Modified Expected Shortfall performs better than the Expected Shortfall and is found to be lower in magnitude. Backtesting results support the superiority of Modified Expected Shortfall when compared with the Expected Shortfall.

Keywords: Coherent risk measure; elliptical distributions; Expected Shortfall; Modified Expected Shortfall.; Primary 91B28; Secondary 91B30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13571-022-00294-1

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