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Properties of the entropic risk measure EVaR in relation to selected distributions
Published 3 Mar 2024 in q-fin.RM and math.PR | (2403.01468v1)
Abstract: Entropic Value-at-Risk (EVaR) measure is a convenient coherent risk measure. Due to certain difficulties in finding its analytical representation, it was previously calculated explicitly only for the normal distribution. We succeeded to overcome these difficulties and to calculate Entropic Value-at-Risk (EVaR) measure for Poisson, compound Poisson, Gamma, Laplace, exponential, chi-squared, inverse Gaussian distribution and normal inverse Gaussian distribution with the help of Lambert function that is a special function, generally speaking, with two branches.
- A. Ahmadi-Javid. Entropic value-at-risk: A new coherent risk measure. Journal of Optimization Theory and Applications, 155:1105–1123, 12 2012.
- A. Ahmadi-Javid and M. Fallah-Tafti. Portfolio optimization with entropic value-at-risk. European Journal of Operational Research, 279(1):225–241, 2019.
- A. Ahmadi-Javid and A. Pichler. An analytical study of norms and Banach spaces induced by the entropic value-at-risk. Mathematics and Financial Economics, 11:1–24, 09 2017.
- A. Axelrod and G. Chowdhary. A dynamic risk form of entropic value at risk. Conference: AIAA Scitech 2019 Forum, 2019.
- O. E. Barndorff-Nielsen. Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of statistics, 24(1):1–13, 1997.
- S. Chennaf and J. Ben Amor. Entropic value at risk to find the optimal uncertain random portfolio. Soft Computing, 27:1–13, 2023.
- On the Lambert W function. Advances in Computational Mathematics, 5:329–359, 01 1996.
- F. Delbaen. Remark on the paper “Entropic value-at-risk: A new coherent risk measure” by Amir Ahmadi-Javid, J. Optim. Theory Appl., 155(3) (2001) 1105–1123”. In P. Barrieu, editor, Risk and Stochastics, pages 151–158. World Scientific, 2019.
- H. Föllmer and A. Schied. Stochastic Finance. An Introduction in Discrete Time. De Gruyter, Berlin, Boston, 2016.
- G. Holton. Value-at-Risk: Theory and Practice. Academic Press, 2003.
- Unwinding the branches of the Lambert W𝑊Witalic_W function. Math. Sci., 21(1):1–7, 1996.
- E. Luxenberg and S. Boyd. Portfolio construction with Gaussian mixture returns and exponential utility via convex optimization. Optim Eng, 2023.
- A. Pichler. A quantitative comparison of risk measures. Annals of Operations Research, Springer, 254(1):251–275, 2017.
- A. Pichler and R. Schlotter. Entropy based risk measure. European Journal of Operational Research, 285(1):223–236, 2020.
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