A Toolkit for Robust Risk Assessment Using F-Divergences

References

• Ahmadi-Javid A (2012) Entropic value-at-risk: A new coherent risk measure. J. Optim. Theory Appl. 155(3):1105–1123.Crossref, Google Scholar
• Ali SM , Silvey SD (1966) A general class of coefficients of divergence of one distribution from another. J. Royal Statist. Soc. B 28(1):131–142.Google Scholar
• Ben-Tal A , El Ghaoui L , Nemirovski A (2009) Robust Optimization (Princeton Univ. Press, NJ). Crossref, Google Scholar
• Ben-Tal A , Den Hertog D , De Waegenaere A , Melenberg B , Rennen G (2013) Robust solutions of optimization problems affected by uncertain probabilities. Management Sci. 59(2):341–357.Link, Google Scholar
• Bertsimas D , Sim M (2004) The price of robustness. Oper. Res. 52(1):35–53.Link, Google Scholar
• Bimpikis K , Markakis MG (2016) Inventory pooling under heavy-tailed demand. Management Sci. 62(6):1800–1813.Link, Google Scholar
• Breuer T , Csiszár I (2016) Measuring distribution model risk. Math. Finance 26(2):395–411.Crossref, Google Scholar
• Clauset A , Shalizi CR , Newman ME (2009) Power-law distributions in empirical data. SIAM Rev. 51(4):661–703.Crossref, Google Scholar
• Csiszár I (1963) Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten. Magyar Tudományos Akadémia Matematikai Kutató Intézetének Közleményei . 8(1-2):85–108.Google Scholar
• Csiszár I , Breuer T (2018) Expected value minimization in information theoretic multiple priors models. IEEE Trans. Inform. Theory 64(6):3957–3974.Crossref, Google Scholar
• Csiszár I , Matúš F (2012) Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities. Kybernetika (Prague) 48(4):637–689.Google Scholar
• Esfahani PM , Kuhn D (2018) Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Programming 171(1-2):115–166.Crossref, Google Scholar
• European Banking Authority (2017) Guide for the Targeted Review of Internal Models (TRIM), version 1.0 (ECB Publication, Frankfurt, Germany). Google Scholar
• Föllmer H , Schied A (2011) Stochastic Finance: An Introduction in Discrete Time , 3rd ed. (Walter de Gruyter, Berlin, Boston).Crossref, Google Scholar
• Frachot A , Moudoulaud O , Roncalli T (2004) Loss distribution approach in practice. Ong M , ed. The Basel Handbook: A Guide for Financial Practitioners (Risk Books, London), 527–554.Google Scholar
• Glasserman P , Xu X (2014) Robust risk measurement and model risk. Quantitative Finance 14(1):29–58.Crossref, Google Scholar
• Hansen LP , Sargent TJ (2011) Robustness (Princeton Univ. Press, NJ). Google Scholar
• Hürlimann W (2009) On the non-life solvency II model. Cruz M , ed. The Solvency II Handbook (Risk Books, London), 349–370.Google Scholar
• Kleiber C , Kotz S (2003) Statistical Size Distributions in Economics and Actuarial Sciences (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Kruse T , Schneider JC , Schweizer N (2019) The joint impact of F-divergences and reference models on the contents of uncertainty sets. Oper. Res. 67(2):428–435.Abstract, Google Scholar
• Lam H (2016) Robust sensitivity analysis for stochastic systems. Math. Oper. Res. 41(4):1248–1275.Link, Google Scholar
• Manski CF (1988) Analog Estimation Methods in Econometrics (Chapman and Hall, New York). Google Scholar
• Morimoto T (1963) Markov processes and the H-theorem. J. Physical. Soc. Japan 18(3):328–331.Crossref, Google Scholar
• Owen AB (2013) Monte Carlo Theory, Methods and Examples. Working paper, Stanford University, Stanford, CA, https://statweb.stanford.edu/∼owen/mc/.Google Scholar
• Pardo L (2005) Statistical Inference Based on Divergence Measures (Chapman and Hall/CRC, Boca Raton, FL). Crossref, Google Scholar
• Pflug GC , Pichler A (2014) Multistage Stochastic Optimization (Springer, New York). Crossref, Google Scholar
• Schneider JC , Schweizer N (2015) Robust measurement of (heavy-tailed) risks: Theory and implementation. J. Econom. Dynamic Control 61:183–203.Crossref, Google Scholar
• Whittle P (1990) Risk-Sensitive Optimal Control (John Wiley & Sons, Hoboken, NJ).Google Scholar