Risk analysis through the half-normal distribution
Bosch Badia, Maria Teresa (Universitat de Girona. Departament d'Economia)
Montllor i Serrats, Joan (Universitat Autònoma de Barcelona. Departament d'Empresa)
Tarrazón Rodón, Ma. Antonia (Universitat Autònoma de Barcelona. Departament d'Empresa)

Date:	2020
Abstract:	We study the applicability of the half-normal distribution to the probability-severity risk analysis traditionally performed through risk matrices and continuous probability-consequence diagrams (CPCDs). To this end, we develop a model that adapts the financial risk measures Value-at-Risk (VaR) and Conditional Value at Risk (CVaR) to risky scenarios that face only negative impacts. This model leads to three risk indicators: The Hazards Index-at-Risk (HIaR), the Expected Hazards Damage (EHD), and the Conditional HIaR (CHIaR). HIaR measures the expected highest hazards impact under a certain probability, while EHD consists of the expected impact that stems from truncating the half-normal distribution at the HIaR point. CHIaR, in turn, measures the expected damage in the case it exceeds the HIaR. Therefore, the Truncated Risk Model that we develop generates a measure for hazards expectations (EHD) and another measure for hazards surprises (CHIaR). Our analysis includes deduction of the mathematical functions that relate HIaR, EHD, and CHIaR to one another as well as the expected loss estimated by risk matrices. By extending the model to the generalised half-normal distribution, we incorporate a shape parameter into the model that can be interpreted as a hazard aversion coefficient.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Half-normal distribution ; Generalised half-normal distribution ; Risk matrices ; Continuous probability-consequence diagrams
Published in:	Mathematics, Vol. 8 Núm. 11 (2020) , p. 2080, ISSN 2227-7390

DOI: 10.3390/math8112080

27 p, 5.2 MB

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