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1. Gain-Loss Hedging and Cumulative Prospect Theory

Author

Bastianello, Lorenzo, Chateauneuf, Alain, and Cornet, Bernard

Subjects
Economics - Theoretical Economics
Abstract

Two acts are comonotonic if they yield high payoffs in the same states of nature. The main purpose of this paper is to derive a new characterization of Cumulative Prospect Theory (CPT) through simple properties involving comonotonicity. The main novelty is a concept dubbed gain-loss hedging: mixing positive and negative acts creates hedging possibilities even when acts are comonotonic. This allows us to clarify in which sense CPT differs from Choquet expected utility. Our analysis is performed under the simpler case of (piece-wise) constant marginal utility which allows us to clearly separate the perception of uncertainty from the evaluation of outcomes.

Published
2023

3. Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules

Author

Bastianello, Lorenzo, Chateauneuf, Alain, and Cornet, Bernard

Subjects
Economics - Theoretical Economics
Abstract

If prices of assets traded in a financial market are determined by non-linear pricing rules, different versions of the Call-Put Parity have been considered. We show that, under monotonicity, parities between call and put options and discount certificates characterize ambiguity-sensitive (Choquet and/or Sipos) pricing rules, i.e., pricing rules that can be represented via discounted expectations with respect to non-additive probability measures. We analyze how non-additivity relates to arbitrage opportunities and we give necessary and sufficient conditions for Choquet and Sipos pricing rules to be arbitrage-free. Finally, we identify violations of the Call-Put Parity with the presence of bid-ask spreads.

Published
2022

5. Linear Exchange Economies

Author

Cornet, Bernard, Maruyama, Toru, Editor-in-Chief, Kusuoka, Shigeo, Series Editor, Grandmont, Jean-Michel, Series Editor, Rockafellar, R. Tyrrell, Series Editor, and Frankowska, Hélène, Series Editor

Published
2023
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10. Put–Call Parities, absence of arbitrage opportunities, and nonlinear pricing rules.

Author

Bastianello, Lorenzo, Chateauneuf, Alain, and Cornet, Bernard

Subjects
PRICES, OPTIONS (Finance), PROBABILITY measures, MARKET prices, DISCOUNT prices
Abstract

When prices of assets traded in a financial market are determined by nonlinear pricing rules, different parities between call and put options have been considered. We show that, under monotonicity, parities between call and put options and discount certificates characterize ambiguity‐sensitive (Choquet and/or Šipoš) pricing rules, that is, pricing rules that can be represented via discounted expectations with respect to non‐additive probability measures. We analyze how nonadditivity relates to arbitrage opportunities and we give necessary and sufficient conditions for Choquet and Šipoš pricing rules to be arbitrage free. Finally, we identify violations of the Call‐Put Parity with the presence of bid–ask spreads. [ABSTRACT FROM AUTHOR]

Published
2024
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15. Existence of financial equilibria in a multi-period stochastic economy

Author

Angeloni, Laura, Cornet, Bernard, Kusuoka, Shigeo, editor, Yamazaki, Akira, editor, Anderson, Robert, editor, Castaing, Charles, editor, Clarke, Frank H., editor, Dierker, Egbert, editor, Duffie, Darrell, editor, Evans, Lawrence C., editor, Fujimoto, Takao, editor, Grandmont, Jean-Michel, editor, Hirano, Norimichi, editor, Hurwicz, Leonid, editor, Ichiishi, Tatsuro, editor, Ioffe, Alexander, editor, Iwamoto, Seiichi, editor, Kamiya, Kazuya, editor, Kawamata, Kunio, editor, Kikuchi, Norio, editor, Maruyama, Toru, editor, Matano, Hiroshi, editor, Nishimura, Kazuo, editor, Richter, Marcel K., editor, Takahashi, Yoichiro, editor, Valadier, Michel, editor, and Yano, Makoto, editor

Published
2006
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17. The Gale–Nikaido–Debreu lemma with discontinuous excess demand

Author

Cornet, Bernard

Abstract

We provide a generalization of the Gale–Nikaido–Debreu’s lemma for discontinuous excess demand in the light of recent work on the existence of equilibria in games with discontinuous payoffs. The standard upper hemicontinuity property of the excess demand is replaced by the weaker concept of “continuous inclusion property” introduced by He and Yannelis (J Math Anal Appl 450(2):1421–1433, 2017) and we allow for the cone Pof admissible prices to be general enough to cover cases for which commodities cannot be freely disposed of.

Published
2024
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26. Fatou's Lemma for Unbounded Gelfand Integrable Mappings

Author

Cornet, Bernard, Martins-Da-Rocha, V. Filipe, Department of economics, University of Kansas, University of Kansas [Lawrence] (KU), Laboratoire d'Economie de Dauphine (LEDa), Institut de Recherche pour le Développement (IRD)-Université Paris Dauphine-PSL, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Dual space, Fatou's lemma, Banach space, Economic equilibrium, Komlós limit, JEL: D - Microeconomics/D.D5 - General Equilibrium and Disequilibrium/D.D5.D50 - General, Gelfand integral, JEL: C - Mathematical and Quantitative Methods/C.C0 - General, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
Abstract

International audience; The objective of this paper is to provide Fatou-type results for sequences of Gelfand integrable mappings defined on a measure space with values in the topological dual of a separable Banach space E. We introduce the assumption of mean weak boundedness that encompasses stronger conditions considered previously. The proof of our Fatou-type results consists in applying successively the scalar version of Komlós' theorem. Since Schmeidler (1970), Fatou's lemma is one of the essential tools in proving the existence of Walrasian equilibria in economic models with a measure space of economic agents as initiated by Aumann (1966). With infinitely many commodities, with commodity space being the topological dual of a separable Banach space, the version of Fatou's lemma with the Gelfand integral applies directly to models of spacial economies (Cornet and Médecin 2000) and models with differentiated commodities (Ostroy and Zame 1994 and Martins-da-Rocha 2003).

Published
2021

32. Equilibrium theory with a measure space of possibly satiated consumers

Author

Cornet, Bernard, Topuzu, Mihaela, and Yildiz, Aysegul

Subjects
Equilibrium (Economics), Consumer preferences, Economics, Mathematics
Abstract

The various existing notions of equilibria proposed to tackle the problem of Walras equilibria ceasing to exist when consumer preferences have been satisfied are discussed. Further, the paper examines an economy with a measure space of consumers and offers a general existence result of equilibria for the existing notions. This result especially extends the result by Hildenbrand on the existence of Walras equilibria.

Published
2003

34. Existence of equilibria for economies with externalities and a measure space of consumers

Author

Cornet, Bernard, Topuzu, Mihaela, CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique (CERMSEM), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), and University of Kansas [Lawrence] (KU)

Subjects
Economics and Econometrics, jel:D62, jel:D51, Equilibrium, Measure space of agents, 05 social sciences, Reference coalitions, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, jel:H23, 0502 economics and business, Externalities, 050206 economic theory, Externalities, Reference coalitions, Measure space of agents, Equilibrium, 050205 econometrics
Abstract

International audience; This paper considers an exchange economy with a measure space of agents and consumption externalities, which take into account two possible external effects on consumersrsquo preferences: dependence upon prices and dependence upon other agentsrsquo consumption. We first consider a model with a general externality mapping and we then treat the particular case of reference coalition externalities, in which the preferences of each agent a are influenced by prices and by the global or the mean consumption of the agents in finitely many (exogenously given) reference coalitions associated with agent a. Our paper provides existence results of equilibria in both models when consumers have transitive preferences. It extends in exchange economies the standard results by Aumann [2], Schmeidler [16], Hildenbrand [12], and previous results by Greenberg et al. [11] for price dependent preferences, Schmeidler [17] for fixed reference coalitions and Noguchi [15] for a more particular concept of reference coalitions. We also mention related results obtained independently by Balder [4].

Published
2018
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37. Fixed-point-like theorems on subspaces

Author

Cornet Bernard and Bich Philippe

Subjects
Applied mathematics. Quantitative methods, T57-57.97, Analysis, QA299.6-433
Abstract

We prove a fixed-point-like theorem for multivalued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems: the fixed-point-like theorem by Hirsch et al. (1990) or Husseini et al. (1990) and the fixed-point theorem by Gale and Mas-Colell (1975) (which generalizes Kakutani's theorem (1941)).

Published
2004

40. Regularity properties of open tangent cones

Author

Cornet, Bernard, Balinski, M. L., editor, Cottle, R. W., editor, Todd, M. J., editor, Dennis, J. E., Jr., editor, Korte, B., editor, Rinnooy Kan, A. H. G., editor, Allgower, E. L., editor, Birge, J. R., editor, Bixby, R. E., editor, Conn, A., editor, Cunningham, W. H., editor, Dixon, L. C. W., editor, Eaves, B. C., editor, Fletcher, R., editor, Grötschel, M., editor, Iri, M., editor, Johnson, D. S., editor, Lemarechal, C., editor, Lovasz, L., editor, McLinden, L., editor, Megiddo, N., editor, Powell, M. J. D., editor, Pulleyblank, W. R., editor, Robinson, S. M., editor, Shanno, D. F., editor, Trotter, L. E., Jr., editor, Wolsey, L., editor, Wright, M. H., editor, Dantzig, G. B., editor, Tucker, A. W., editor, Wolfe, P., editor, Cornet, B., editor, Nguyen, V. H., editor, and Vial, J. P., editor

Published
1987
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42. Eliminating useless portfolios in financial economies with constraints

Author

Aouani, Zaier, Cornet, Bernard, College of Business and Economics, Qatar University, Qatar University, Department of Economics [Astana], Nazarbayev University [Kazakhstan], Centre d'économie de la Sorbonne (CES), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), Paris School of Economics (PSE), École des Ponts ParisTech (ENPC)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-École des hautes études en sciences sociales (EHESS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
Useless-free financial structure, Werner useless portfolios, Equivalent financial structures, Redundant assets, JEL: D - Microeconomics/D.D5 - General Equilibrium and Disequilibrium/D.D5.D52 - Incomplete Markets, JEL: D - Microeconomics/D.D5 - General Equilibrium and Disequilibrium/D.D5.D53 - Financial Markets, Financial exchange economy, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, Useless portfolios, JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C62 - Existence and Stability Conditions of Equilibrium, Restricted participation
Abstract

International audience; When financial investors’ portfolio holdings are unconstrained, financial economies are assumed, w.l.o.g., to have no redundant assets. Indeed, eliminating redundant assets allows to replace the initial financial structure by an equivalent one, i.e., one that has the same consumption equilibria. Moreover, at the end of the process, absence of redundant assets guarantees that the set of admissible portfolio allocations is bounded, a fundamental property for the existence of equilibria. In the presence of institutional (exogenous) portfolio constraints, eliminating redundant assets is not innocuous anymore since bounded arbitrage may persist at equilibrium, the law of one price does not hold, and some zero-income portfolios may not be free. The goal of the paper is to replace the elimination of redundant assets by the elimination of useless portfolios, a process that eliminates in particular Werner useless portfolios, but needs to go beyond to obtain the boundedness of the set of admissible portfolio allocations at the end of the purification process. Moreover, the elimination process is carried out without affecting the set of consumption equilibria, hence replacing at each step the financial structure by an equivalent one.

Published
2017
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46. A Remark on the Set of Arbitrage-Free Prices in a Multi-period Model

Author

Cornet, Bernard, Ranjan, Abhishek, Centre d'économie de la Sorbonne (CES), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), Paris School of Economics (PSE), École des Ponts ParisTech (ENPC)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-École des hautes études en sciences sociales (EHESS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and Ce travail a bénéficié d'une aide de l'Etat gérée par l'Agence Nationale de la Recherche au titre du programme « Investissements d'avenir » portant la référence ANR-10-LABX-93-01.This work was supported by the French National Research Agency, through the program Investissements d'Avenir, ANR-10-LABX-93-01.

Subjects
JEL: D - Microeconomics/D.D5 - General Equilibrium and Disequilibrium/D.D5.D53 - Financial Markets, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, arbitrage
Abstract

International audience; We study the convexity property of the set Q[subscript F] of arbitrage-free prices of a multi-period financial structure F. The set of arbitrage-free prices is shown to be a convex cone under conditions on the financial structure F that hold in particular for short-lived assets. Furthermore, we provide examples of equivalent financial structures F and F' such that Q[subscript F] is a convex cone, but Q[subscript F'] is neither convex nor a cone.

Published
2013
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47. Editorial

Author

Cornet, Bernard, University of Kansas [Lawrence] (KU), Centre d'économie de la Sorbonne (CES), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), Paris School of Economics (PSE), École des Ponts ParisTech (ENPC)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-École des hautes études en sciences sociales (EHESS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
[SHS.ECO]Humanities and Social Sciences/Economics and Finance, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2010
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49. Editorial

Author

Cornet, Bernard, University of Kansas [Lawrence] (KU), Centre d'économie de la Sorbonne (CES), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), Paris School of Economics (PSE), École des Ponts ParisTech (ENPC)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-École des hautes études en sciences sociales (EHESS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
[SHS.ECO]Humanities and Social Sciences/Economics and Finance, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2009
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50. Editorial

Author

Cornet, Bernard, University of Kansas [Lawrence] (KU), Centre d'économie de la Sorbonne (CES), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), Paris School of Economics (PSE), École des Ponts ParisTech (ENPC)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS)-École des hautes études en sciences sociales (EHESS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
[SHS.ECO]Humanities and Social Sciences/Economics and Finance, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2008
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