References. H. Föllmer, A. Schied, Stochastic Finance (3rd Ed.) de Gruyter 2011 (chapters 4 and 11)
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1 General references on risk measures P. Embrechts, R. Frey, A. McNeil, Quantitative Risk Management, (2nd Ed.) Princeton University Press, 2015 H. Föllmer, A. Schied, Stochastic Finance (3rd Ed.) de Gruyter 2011 (chapters 4 and 11) E. Jondeau, S.-H. Poon, M. Rockinger, Financial Modeling Under Non-Gaussian Distributions, Springer 2007 (chapters 2,6,8,9) H. Föllmer, S. Weber The Axiomatic Approach to Risk Measures for Capital Determination. Annual Review of Financial Economics, 2015 An introduction to coherent risk measures Giacomo Scandolo (Unifi) 1 / 5
2 On VaR and ES Duffie, Pan. An overview of value-at-risk. The Journal of Derivatives, n.4(3), 1997 Marinelli, D Addona, Rachev. A comparison of some univariate models for Value-at-Risk and Expected Shortfall. International Journal of Theoretical and Applied Finance, n.10, Bertsimas, Lauprete, Samarov. Shortfall as a risk measure: properties, optimization and applications. Journal of Economic Dynamics and Control, n.28(7), 2004 Rockafellar, Uryasev. Conditional value-at-risk for general loss distributions. Journal of Banking and Finance, n.26(7), 2002 On the optimization of VaR and ES Rockafellar, Uryasev. Optimization of conditional value-at-risk, Journal of Risk, 2, 2000 Gaivoronski, Pflug. Value-at-risk in portfolio optimization: properties and computational approach, Journal of Risk, 7, 2005 An introduction to coherent risk measures Giacomo Scandolo (Unifi) 2 / 5
3 On coherent risk measures Artzner, Delbaen, Eber, Heath. Coherent measures of risk. Mathematical finance, no.9(3), Delbaen. Coherent risk measures on general probability spaces. Advances in finance and stochastics. Springer, Föllmer, Schied Convex measures of risk and trading constraints, Finance and Stochastics 6(4), 2002 Dhaene, Laeven, Vanduffel, Darkiewicz, Goovaerts. Can a coherent risk measure be too subadditive? Journal of Risk and Insurance, 75(2), 2008 On the coherence of ES Acerbi, Tasche. On the coherence of expected shortfall, Journal of Banking and Finance 26, 2002 Embrechts, Wang. Seven Proofs for the Subadditivity of Expected Shortfall. Working paper, 2015 An introduction to coherent risk measures Giacomo Scandolo (Unifi) 3 / 5
4 On deviation-based risk measures Fischer. Risk capital allocation by coherent risk measures based on one-sided moments. Insurance: Mathematics and Economics, 32(1), 2003 Rockafellar, Uryasev, Zabarankin. Generalized deviations in risk analysis. Finance and Stochastics, 10(1), On spectral risk measures Acerbi. Spectral measures of risk: a coherent representation of subjective risk aversion. Journal of Banking and Finance, 26(7), 2002 Adam, Houkari, Laurent. Spectral risk measures and portfolio selection. Journal of Banking and Finance, 32(9), 2008 On concave distortion Hürlimann. Distortion risk measures and economic capital. North American Actuarial Journal, 8(1), On generalized quantiles and elicitable risk measures Bellini, Klar, Müller, Rosazza. Generalized quantiles as risk measures. Insurance: Mathematics and Economics, 54, Ziegel. Coherence and elicitability Mathematical Finance, 2014 An introduction to coherent risk measures Giacomo Scandolo (Unifi) 4 / 5
5 On comonotonic additivity Dhaene, Vanduffel, Goovaerts, Kaas, Tang, Vyncke. Risk measures and comonotonicity: a review. Stoch. Models 22(4), 2006 Kusuoka. On law invariant coherent risk measures Advances Math. Econ 3, 2001 On plug-in estimators for risk measures Belomestny, Krätschmer. Central limit theorems for law-invariant coherent risk measures. Journal of Applied Probability 49.1, 2012 Pflug, Wozabal. Asymptotic distribution of law-invariant risk functionals. Finance and Stochastics 14(3), 2010 On robustness of risk estimators P. Huber. Robust Statistics, Springer Berlin, Cont, Deguest, Scandolo. Robustness and sensitivity analysis of risk measurement procedures, Quantitative Finance 10(6), 2010 Krätschmer, Schied, Zähle. Comparative and qualitative robustness for law invariant risk measures, Finance and Stochastics 18(2), 2014 An introduction to coherent risk measures Giacomo Scandolo (Unifi) 5 / 5
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