Surplus-Invariant Risk Measures

Published Online:https://doi.org/10.1287/moor.2019.1035

References

  • [1] Aliprantis CD, Burkinshaw O (2003) Locally Solid Riesz Spaces and Applications to Economics, 2nd ed. (American Mathematical Society, Providence, RI).CrossrefGoogle Scholar
  • [2] Aliprantis CD, Burkinshaw O (2006) Positive Operators (Springer, Berlin).CrossrefGoogle Scholar
  • [3] Artzner P, Delbaen F, Eber JM, Heath D (1996) A characterization of measures of risk. Technical Report 1186, Cornell University, Ithaca, NY.Google Scholar
  • [4] Artzner P, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.CrossrefGoogle Scholar
  • [5] Bernardo A, Ledoit O (2000) Gain, loss and asset pricing. J. Political Econom. 108(1):144–172.CrossrefGoogle Scholar
  • [6] Bignozzi V, Burzoni M, Munari C (2019) Risk measures based on benchmark loss distributions. J. Risk Insurance 87(2):437–475.Google Scholar
  • [7] Brannath W, Schachermayer W (1999) A bipolar theorem for L+0(Ω,ℱ,𝒫). Séminaire de Probabilités, vol. 33 (Springer, Berlin), 349–354.Google Scholar
  • [8] Carr P, Geman H, Madan DB (2001) Pricing and hedging in incomplete markets. J. Financial Econom. 62(1):131–167.CrossrefGoogle Scholar
  • [9] Cerreia-Vioglio S, Maccheroni F, Marinacci M, Montrucchio L (2011) Risk measures: rationality and diversification. Math. Finance 21(4):743–774.Google Scholar
  • [10] Cochrane J, Saá-Requejo J (2000) Beyond arbitrage:Good-deal asset price bounds in incomplete markets. J. Political Econom. 108(1):79–119.CrossrefGoogle Scholar
  • [11] Cont R, Deguest R, He X (2013) Loss-based risk measures. Statist. Risk Model. 30(2):133–167.CrossrefGoogle Scholar
  • [12] Delbaen F (2002) Coherent risk measures on general probability spaces. Sandmann K, Schönbucher P, eds. Advances in Finance and Stochastics: Essays in Honour of Dieter Sondermann (Springer, Berlin), 1–37.Google Scholar
  • [13] Delbaen F (2009) Risk measures for non-integrable random variables. Math. Finance 19(2):329–333.CrossrefGoogle Scholar
  • [14] Delbaen F, Owari K (2019) Convex functions on dual Orlicz spaces. Positivity 23(5):1051–1064.CrossrefGoogle Scholar
  • [15] Drapeau S, Kupper M (2013) Risk preferences and their robust representations. Math. Oper. Res. 38(1):28–62.LinkGoogle Scholar
  • [16] Edgar G, Sucheston L (1992) Stopping Times and Directed Processes (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [17] Filipović D, Svindland G (2012) The canonical model space for law-invariant convex risk measures is L1. Math. Finance 22(3):585–589.CrossrefGoogle Scholar
  • [18] Föllmer H, Schied A (2017) Stochastic Finance: An Introduction in Discrete Time, 4th ed. (de Gruyter, Berlin).Google Scholar
  • [19] Gao N, Xanthos F (2018) On the C-property and w*-representations of risk measures. Math. Finance 28(2):748–754.CrossrefGoogle Scholar
  • [20] Gao N, Leung D, Xanthos F (2019) Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measures. Studia Mathematica 249:329–347.CrossrefGoogle Scholar
  • [21] Gao N, Troitsky V, Xanthos F (2017) Uo-convergence and its applications to Cesàro means in Banach lattices. Israel J. Math. 220(2):649–689.CrossrefGoogle Scholar
  • [22] Gao N, Leung D, Munari C, Xanthos F (2018) Fatou property, representation and extension of law-invariant risk measures on general Orlicz spaces. Finance Stochastics 22(2):395–415.CrossrefGoogle Scholar
  • [23] He X, Peng X (2018) Surplus-invariant, law-invariant, and conic acceptance sets must be the sets induced by Value at Risk. Oper. Res. 66(5):1268–1275.LinkGoogle Scholar
  • [24] Koch-Medina P, Moreno-Bromberg S, Munari C (2015) Capital adequacy tests and limited liability of financial institutions. J. Banking Finance 51(February):93–102.CrossrefGoogle Scholar
  • [25] Koch-Medina P, Munari, C (2016) Unexpected shortfalls of Expected Shortfall: Extreme default profiles and regulatory arbitrage. J. Bank. Finance 62(January):141–151.CrossrefGoogle Scholar
  • [26] Koch-Medina P, Munari C, Šikić M (2017) Diversification, protection of liability holders and regulatory arbitrage. Math. Financial Econom. 11(1):63–83.CrossrefGoogle Scholar
  • [27] Koch-Medina P, Munari C, Šikić M (2018) A simple characterization of tightness for convex solid sets of positive random variables. Positivity 22(2):1015–1022.CrossrefGoogle Scholar
  • [28] Liebrich FB, Svindland G (2017) Model spaces for risk measures. Insurance Math. Econom. 77(November):150–165.CrossrefGoogle Scholar
  • [29] Liu F, Wang R (2016) A theory for measures of tail risk. Working paper, Central University of Finance and Economics, Beijing, China.Google Scholar
  • [30] Madan DB, Cherny A (2010) Markets as a counterparty: An introduction to conic finance. Internat. J. Theoret. Appl. Finance 13(8):1149–1177.CrossrefGoogle Scholar
  • [31] Maggis M, Meyer-Brandis T, Svindland G (2018) The Fatou closedness under model uncertainty. Positivity 22(5):1325–1343.CrossrefGoogle Scholar
  • [32] Meyer-Nieburg P (1991) Banach Lattices (Springer, Berlin).CrossrefGoogle Scholar
  • [33] Munari C (2015) Measuring risk beyond the cash-additive paradigm. Doctoral dissertation, ETH Zurich, Zurich, Switzerland.Google Scholar
  • [34] Pichler A (2013) The natural Banach space for version independent risk measures. Insurance Math. Econom. 53(2):405–415.CrossrefGoogle Scholar
  • [35] Staum J (2013) Excess invariance and shortfall risk measures. Oper. Res. Lett. 41(1):47–53.CrossrefGoogle Scholar
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