A Unified Approach to Time Consistency of Dynamic Risk Measures and Dynamic Performance Measures in Discrete Time

References

• Acciaio B, Penner I (2011) Dynamic risk measures. Di Nunno G, Øksendal B, eds. Advanced Mathematical Methods for Finance (Springer, Berlin), 1–34.Crossref, Google Scholar
• Acciaio B, Föllmer H, Penner I (2012) Risk assessment for uncertain cash flows: Model ambiguity, discounting ambiguity, and the role of bubbles. Finance and Stochastics 16(4):669–709.Crossref, Google Scholar
• Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
• Artzner P, Delbaen F, Eber JM, Heath D, Ku H (2007) Coherent multiperiod risk adjusted values and Bellman’s principle. Ann. Oper. Res. 152(1):5–22.Crossref, Google Scholar
• Barron EN, Cardaliaguet P, Jensen R (2003) Conditional essential suprema with applications. Appl. Math. Optim. 48(3):229–253.Crossref, Google Scholar
• Biagini S, Bion-Nadal J (2014) Dynamic quasi-concave performance measures. J. Math. Econom. 55:143–153.Crossref, Google Scholar
• Bielecki TR, Cialenco I, Chen T (2015) Dynamic conic finance via backward stochastic difference equations. SIAM J. Finan. Math. 6(1):1068–1122.Crossref, Google Scholar
• Bielecki TR, Cialenco I, Pitera M (2015) Dynamic limit growth indices in discrete time. Stochastic Models 31(3):494–523.Crossref, Google Scholar
• Bielecki TR, Cialenco I, Pitera M (2017) A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective. Probab., Uncertainty and Quant. Risk 2(1):Article 1.Crossref, Google Scholar
• Bielecki TR, Cialenco I, Zhang Z (2014) Dynamic coherent acceptability indices and their applications to finance. Math. Finance 24(3):411–441.Crossref, Google Scholar
• Bielecki TR, Cialenco I, Drapeau S, Karliczek M (2016) Dynamic assessment indices. Stochastics: An Internat. J. Probab. Stochastic Processes 88(1):1–44.Crossref, Google Scholar
• Bielecki TR, Cialenco I, Iyigunler I, Rodriguez R (2013) Dynamic conic finance: Pricing and hedging via dynamic coherent acceptability indices with transaction costs. Internat. J. Theoret. Appl. Finance 16(1):1350002.Crossref, Google Scholar
• Cheridito P, Kromer E (2013) Reward-risk ratio. J. Investment Strategies 3(1):1–16.Crossref, Google Scholar
• Cheridito P, Kupper M (2011) Composition of time-consistent dynamic monetary risk measures in discrete time. Internat. J. Theoret. Appl. Finance 14(1):137–162.Crossref, Google Scholar
• Cheridito P, Li T (2009) Risk measures on Orlicz hearts. Math. Finance 19(2):189–214.Crossref, Google Scholar
• Cheridito P, Delbaen F, Kupper M (2006) Dynamic monetary risk measures for bounded discrete-time processes. Electron. J. Probab. 11(3):57–106.Crossref, Google Scholar
• Cherny A (2010) Risk-reward optimization with discrete-time coherent risk. Math. Finance 20(4):571–595.Crossref, Google Scholar
• Cherny A, Madan D (2009) New measures for performance evaluation. Rev. Financial Stud. 22(7):2571–2606.Crossref, Google Scholar
• Delbaen F (2006) The structure of m-stable sets and in particular of the set of risk neutral measures. In Memoriam Paul-André Meyer: Séminaire de Probabilités XXXIX, Lecture Notes in Math., Vol. 1874 (Springer, Berlin), 215–258.Crossref, Google Scholar
• Detlefsen K, Scandolo G (2005) Conditional and dynamic convex risk measures. Finance and Stochastics 9(4):539–561.Crossref, Google Scholar
• Epstein L, Schneider M (2003) Recursive multiple-priors. J. Econom. Theory 113(1):1–31.Crossref, Google Scholar
• Filipovic D, Kupper M, Vogelpoth N (2009) Separation and duality in locally L0-convex modules. J. Functional Anal. 256:3996–4029.Crossref, Google Scholar
• Föllmer H, Penner I (2006) Convex risk measures and the dynamics of their penalty functions. Statist. Decisions 24(1):61–96.Google Scholar
• Föllmer H, Schied A (2010) Convex risk measures. Encyclopedia of Quant. Finance 10(2):143–157.Google Scholar
• Hanany E, Klibanoff P (2009) Updating ambiguity averse preferences. The BE J. Theoret. Econom. 9(1):1935–1704.Google Scholar
• Karatzas I, Shreve SE (1998) Methods of Mathematical Finance (Springer, New York).Crossref, Google Scholar
• Penner I (2007) Dynamic Convex Risk Measures: Time Consistency, Prudence, and Sustainability. PhD thesis, Humboldt Universität zu Berlin.Google Scholar
• Riedel F (2004) Dynamic coherent risk measures. Stochastic Process. Appl. 112(2):185–200.Crossref, Google Scholar
• Rosazza Gianin E (2006) Risk measures via g-expectations. Insurance: Math. Econom. 39(1):19–34.Crossref, Google Scholar
• Rosazza Gianin E, Sgarra E (2013) Acceptability indexes via g-expectations: An application to liquidity risk. Math. Finance 7:457–475.Crossref, Google Scholar
• Ruszczyński A (2010) Risk-averse dynamic programming for Markov decision processes. Math. Programming 125(2):235–261.Crossref, Google Scholar
• Ruszczyński A, Shapiro A (2006) Conditional risk mappings. Math. Oper. Res. 31(3):544–561.Link, Google Scholar
• Tutsch S (2008) Update rules for convex risk measures. Quant. Finance 8(8):833–843.Crossref, Google Scholar