Uniqueness of Convex-Ranged Probabilities and Applications to Risk Measures and Games
References
- [1] (2006) Infinite Dimensional Analysis: A Hitchhiker’s Guide (Springer, Berlin).Google Scholar
- [2] (2004) On the uniqueness of convex-ranged probabilities. Decision Econom. Finance 27(1):81–85.Crossref, Google Scholar
- [3] (2005) Ambiguity, measurability and multiple priors. Econom. Theory 26(4):995–1006.Crossref, Google Scholar
- [4] (2021) Bipolar behavior of submodular, law-invariant capacities. Statist. Risk Model. 38(3–4):65–70.Crossref, Google Scholar
- [5] (2008) Exact capacities and star-shaped distorted probabilities. Math. Social Sci. 56(2):185–194.Crossref, Google Scholar
- [6] (1974) Value of Non-Atomic Games (Princeton University Press, Princeton, NJ).Google Scholar
- [7] (2021) Law-invariant functionals that collapse to the mean. Insurance Math. Econom. 98(1):83–91.Crossref, Google Scholar
- [8] (1983) Theory of Charges: A Study of Finitely Additive Measures (Academic Press, London).Google Scholar
- [9] (2004) Choquet insurance pricing: A caveat. Math. Finance 14(3):481–485.Crossref, Google Scholar
- [10] (2002) Coherent risk measures on general probability spaces. Sandmann K, Schönbucher PJ, eds. Advances in Finance and Stochastics (Springer, Berlin), 1–37.Crossref, Google Scholar
- [11] (1994) Non-Additive Measure and Integral (Springer, Dordrecht, Netherlands).Crossref, Google Scholar
- [12] (2023) The set structure of precision. Proc. Machine Learn. Res. 215:165–176.Google Scholar
- [13] (1987) Convex Analysis and Variational Problems (Society for Industrial and Applied Mathematics, Philadelphia).Google Scholar
- [14] (2001) Subjective probabilities on subjectively unambiguous events. Econometrica 69(2):265–306.Crossref, Google Scholar
- [15] (2016) Stochastic Finance: An Introduction in Discrete Time (De Gruyter, Berlin).Crossref, Google Scholar
- [16] (2005) Law invariant convex risk measures. Adv. Math. Econom. 7:42–53.Google Scholar
- [17] (2001) Risk, ambiguity, and the separation of utility and beliefs. Math. Oper. Res. 26(4):864–890.Link, Google Scholar
- [18] (1934) Inequalities (Cambridge University Press, Cambridge, UK).Google Scholar
- [19] (1997) On the existence of subjective upper and lower probabilities. Math. Oper. Res. 22(1):165–185.Link, Google Scholar
- [20] (2006) Law invariant risk measures have the Fatou property. Adv. Math. Econom. 9:49–71.Crossref, Google Scholar
- [21] (1996) Symmetric, coherent, Choquet capacities. Ann. Statist. 24(3):1250–1264.Crossref, Google Scholar
- [22] (2007) Subjective probabilities on “small” domains. J. Econom. Theory 133(1):236–265.Crossref, Google Scholar
- [23] (2022) Are reference measures of law-invariant functionals unique? Working paper, Amsterdam.Google Scholar
- [24] (2022) Law-invariant functionals that collapse to the mean: Beyond convexity. Math. Financial Econom. 16(3):447–480.Crossref, Google Scholar
- [25] (1967) Rearrangement-invariant Banach function spaces. Queen’s Papers Pure Appl. Math. 10:83–144.Google Scholar
- [26] (1999) Upper probabilities and additivity. Sankhya A 61(3):358–361.Google Scholar
- [27] (2000) A uniqueness theorem for convex-ranged probabilities. Decision Econom. Finance 23:121–132.Crossref, Google Scholar
- [28] (2002) Probabilistic sophistication and multiple priors. Econometrica 70(2):755–764.Crossref, Google Scholar
- [29] (2004) Introduction to the mathematics of ambiguity. Gilboa I, ed. Uncertainty in Economic Theory: A Collection of Essays in Honor of David Schmeidler’s 65th Birthday (Routledge, London), 46–107.Crossref, Google Scholar
- [30] (1999) Capacities and probabilistic beliefs: A precarious coexistence. Math. Social Sci. 38(2):197–213.Crossref, Google Scholar
- [31] (1972) Cores of exact games I. J. Math. Anal. Appl. 40(1):214–225.Crossref, Google Scholar
- [32] (2008) Finitistic and frequentistic approximation of probability measures with or without σ-additivity. Studia Logica 89(2):257–283.Crossref, Google Scholar
- [33] (1920) Sur les fonctions convexes mesurables. Fundamenta Mathematicae 1:125–129.Crossref, Google Scholar
- [34] (2010) Continuity properties of law-invariant (quasi-)convex risk functions on L∞. Math. Financial Econom. 3(1):39–43.Crossref, Google Scholar
- [35] (2017) Uniqueness theorems for finitely additive probabilities on quantum structures. Math. Slovaca 67(3):685–690.Crossref, Google Scholar
- [36] (2002) Subjective ambiguity, expected utility and Choquet expected utility. Econom. Theory 20(1):159–181.Crossref, Google Scholar

