Risk Measures: Rationality and Diversification (2010)
Maccheroni, Fabio; Dept. Of Decision Sciences, U. Bocconi; Fabio.maccheroni@unibocconi.it, Cerreia-Vioglio, Simone; Dept. Of Economics, Columbia University; Simone.cerreia@gmail.com, Marinacci, Massimo; Collegio Carlo Alberto, U. Torino; Massimo.marinacci@carloalberto.org, Montrucchio, Luigi; Collegio Carlo Alberto, U. Torino; Luigi.montrucchio@econ.unito.it
Risk assessment is a fundamental activity for both regulators and agents in financial markets. The problem of a formal definition of a risk measure and of the economic and mathematical properties it...
Printed in U.S.A. RISK, AMBIGUITY, AND THE SEPARATION OF UTILITY AND BELIEFS (2008)
Paolo Ghirardato, Massimo Marinacci
We introduce a general model of static choice under uncertainty, arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs. Most of the nonexpected...
Larry G. Epstein, Massimo Marinacci
Epstein gratefully acknowledges the …nancial support of the NSF (award SES-0611456)
Coarse contingencies and ambiguity (2007)
Larry G. Epstein; Boston University, Massimo Marinacci; Universita Di Torino, Kyoungwon Seo; University Of Rochester
The paper considers an agent who must choose an action today under uncertainty about the consequence of any chosen action but without having in mind a complete list of all the contingencies that...
Coarse contingencies and ambiguity (2007)
Larry G. Epstein; Boston University, Massimo Marinacci; Universita Di Torino, Kyoungwon Seo; University Of Rochester
[This item is a preserved copy. To view the original, visit http://econtheory.org/] The paper considers an agent who must choose an action today under uncertainty about the consequence of any chosen...
Paolo Ghirardato, Paolo Ghirardato, Paolo Ghirardato, Fabio Maccheroni, Fabio Maccheroni, ...
The objective of this paper is to show how ambiguity, and a decision maker (DM)’s response to it, can be modelled formally in the context of a very general decision model. In the first part of the...
Maxmin Expected Utility, Range Convexity (2007)
Paolo Ghirardato, Paolo Ghirardato, Paolo Ghirardato, Massimo Marinacci, Massimo Marinacci, Massimo Marinacci
We show that range convexity of beliefs, a ‘technical ’ condition that appears naturally in axiomatizations of preferences in a Savage-like framework, imposes some unexpected restrictions when...
Ambiguity Made Precise: A Comparative (2007)
Paolo Ghirardato, Paolo Ghirardato, Paolo Ghirardato, Massimo Marinacci, Massimo Marinacci, Massimo Marinacci
Foundation
HOW TO CUT A CAKE HEALTHILY (2007)
Fabio Maccheroni, Fabio Maccheroni, Fabio Maccheroni, Massimo Marinacci, Massimo Marinacci, ...
How to cut a cake healthily
A Subjective Spin on Roulette Wheels ∗ (2007)
Paolo Ghirardato, Paolo Ghirardato, Paolo Ghirardato, Fabio Maccheroni, Fabio Maccheroni, ...
We provide a behavioral foundation to the notion of ‘mixture ’ of acts, which is used to great advantage in the decision setting introduced by Anscombe and Aumann [1]. Our construction allows one...
Larry G. Epstein, Massimo Marinacci, Kyoungwon Seo
The paper considers an agent who must choose an action today under uncertainty about the consequence of any chosen action but without having in mind a complete list of all the contingencies that...
A strong law of large numbers for capacities (2005)
Maccheroni, Fabio, Marinacci, Massimo
We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the...
Monotone continuous multiple priors (2005)
Chateauneuf, Alain, Macheronni, Fabio, Marinacci, Massimo, Tallon, Jean-Marc
We show that the monotone continuity condition introduced by Arrow (1970) is the behavioral counterpart of countable additivity and weak compactness of the set of priors in a maxmin expected utility...
Monotone continuous multiple priors (2005)
Chateauneuf, Alain, Macheronni, Fabio, Marinacci, Massimo, Tallon, Jean-Marc
We show that the monotone continuity condition introduced by Arrow (1970) is the behavioral counterpart of countable additivity and weak compactness of the set of priors in a maxmin expected utility...
A Smooth Model of Decision Making Under Ambiguity (2005)
Peter Klibanoff, Massimo Marinacci, Sujoy Mukerji, E. Dekel, D. Fudenberg, ...
for helpful discussions and suggestions. We also thank three referees and A. Postlewaite, the co-editor, for offering very useful comments and advice. We also thank a number of seminar and conference...
UNIVERSITY OF ROCHESTER COARSE CONTINGENCIES (2005)
Larry G, Massimo Marinacci, Larry G. Epstein, Massimo Marinacci, Mark Machina, Luigi Montrucchio
The paper considers an agent who must choose an action today under uncertainty about the consequence of any chosen action but without having in mind a complete list of all the contingencies that...
make-position creates an row col coordinate that represents a position on the board (2005)
Larry G. Epstein, Jawwad Noor, Alvaro Sandroni, Conversations Mark Machina, Massimo Marinacci, Joseph Perktold, ...
This paper models an agent in a multi-period setting who does not update according to Bayes ’ Rule, and who is self-aware and anticipates her updating behavior when formulating plans....
Paolo Ghirardato, Fabio Maccheroni, Massimo Marinacci
We dedicate this paper—an extended version of which was previously circulated with the title ‘‘Ambiguity
Theory of Reputational Cheap (2003)
Marco Ottaviani A, Markus Brunnermeier, Vincent Crawford, Eddie Dekel, ...
This paper studies strategic communication by an expert who is concerned about appearing to be well informed. The expert is assumed to observe a private signal with a simple and particularly...
Theory of Reputational Cheap (2003)
Marco Ottaviani A, Markus Brunnermeier, Vincent Crawford, Eddie Dekel, ...
This paper studies strategic communication by an expert who is concerned about appearing to be well informed. The expert is assumed to observe a private signal with a simple and particularly...
Ambiguity made precise: A comparative foundation (2002)
Paolo Ghirardato, Massimo Marinacci
Simon Grant and Peter Wakker for helpful comments and discussions. Our greatest debt of gratitude is however to Larry Epstein, who sparked our interest on this subject with his paper (Epstein 1997),...
Paolo Ghirardato, Massimo Marinacci, Paolo Ghirardato, Massimo Marinacci
We introduce a general model of static choice under uncertainty, arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs. Most of the non-expected...
Risk, ambiguity, and the separation of utility and beliefs (2001)
Paolo Ghirardato, Paolo Ghirardato, Paolo Ghirardato, Massimo Marinacci, Massimo Marinacci, Massimo Marinacci
We introduce and characterize axiomatically a general model of static choice under uncertainty, which is possibly the weakest model in which a separation of cardinal utility and a representation of...
Larry G. Epstein, Massimo Marinacci, Tu Games, Larry G. Epstein, Massimo Marinacci
For non-atomic TU games ν satisfying suitable conditions, the core can be determined by computing appropriate derivatives of ν. Further, such computations yield one of two stark conclusions: either...
Upper probability and additivity (1999)
SUMMARY. We show that symmetric and coherent Choquet capacities, a class of upper probabilities arising in many robustness models, are additive under a fairly mild condition.
A strong law of large numbers for capacities.
Fabio Maccheroni, Massimo Marinacci
We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the...
Larry Epstein, Massimo Marinacci
The paper considers an agent who must choose an action today under uncertainty about the consequence of any chosen action but without having in mind a complete list of all the contingencies that...
A Smooth Model of Decision Making under Ambiguity
Peter Klibanoff, Massimo Marinacci, Sujoy Mukerji
We propose and characterize a model of preferences over acts such that the decision maker prefers act f to act g if and only if Eμφ( Eπu○f) ⩾ Eμφ( Eπu○g), where E is the expectation...
Massimo Marinacci, Luigi Montrucchio
TV games, vN-M stable sets, large cores, bargaining sets,
Risk, Ambigity and the Separation of Utility and Beliefs
Ghirardato, Paolo, Marinacci, Massimo
We introduce and characterize axiomatically a general model of static choice under uncertainty, which is possibly the weakest model in which a separation of cardinal utility and a representation of...
A Subjective Spin on Roulette Wheels
Ghirardato, Paolo, Maccheroni, Fabio, Marinacci, Massimo, Siniscalchi, Marciano
Mutual Absolute Continuity of Multiple Priors
Larry G. Epstein, Massimo Marinacci
This note provides a behavioral characterization of mutually absolutely continuous multiple priors.
Cores of Non-Atomic Market Games
Massimiliano Amarante, Fabio Maccheroni, Massimo Marinacci, Luigi Montrucchio
We study the cores of non-atomic market games, a class of transferable utility co- operative games introduced by Aumann and Shapley [2], and, more in general, of those games that admit a...
Ambiguity Aversion, Robustness, and the Variational Representation of Preferences
Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini
Ambiguity; Robustness, Multiplier Preferences
Portfolio Selection with Monotone Mean-Variance Preferences
Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini, Marco Taboga
We propose a portfolio selection model based on a class of monotone preferences that coincide with mean-variance preferences on their domain of monotonicity, but differ where mean-variance...
Larry G. Epstein, Massimo Marinacci, Seo Kyoungwon
The paper considers an agent who must choose an action today under uncertainty about the consequence of any chosen action but without having in mind a complete list of all the contingencies that...
Dynamic Variational Preferences
Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini
We introduce and axiomatize dynamic variational preferences, the dynamic version of the variational preferences we axiomatized in [21], which generalize the multiple priors preferences of Gilboa and...
On Concavity and Supermodularity
Massimo Marinacci, Luigi Montrucchio
Concavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members...
Recursive Smooth Ambiguity Preferences
Peter Klibanoff, Massimo Marinacci, Sujoy Mukerji
This paper axiomatizes an intertemporal version of the Smooth Ambiguity decision model developed in Klibanoff, Marinacci, and Mukerji (2005). A key feature of the model is that it achieves a...
Unique Solutions of Some Recursive Equations in Economic Dynamics
Massimo Marinacci, Luigi Montrucchio
We study unique and globally attracting solutions of a general nonlinear equation that has as special cases some recursive equations widely used in Economics.
Monotone continuous multiple priors
Alain Chateauneuf, Fabio Macheronni, Massimo Marinacci, Jean-Marc Tallon
We show that the monotone continuity condition introduced by Arrow (1970) is the behavioral counterpart of countable additivity and weak compactness of the set of priors in a maxmin expected utility...
Social Decision Theory: Choosing within and between Groups
Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini
We introduce a theoretical framework in which to study interdependent preferences, where the outcome of others affects the preferences of the decision maker. The dependence may take place in two...
Objective and Subjective Rationality in a Multiple Prior Model
Itzhak Gilboa, Fabio Maccheroni, Massimo Marinacci, David Schmeidler
A decision maker is characterized by two binary relations. The first reflects decisions that are rational in an “objective” sense: the decision maker can convince others that she is right in...
Risk, Ambiguity and the Separation of Utility and Beliefs
Paolo Ghirardato, Massimo Marinacci
The theory of subjective expected utility (SEU) has been extended in many recent works, allowing ambiguity to matter for choice. However, a fully satisfactory and general notion of ambiguity...
Probabilistic sophistication and multiple priors.
We show that under fairly mild conditions, a maximin expected utility preference relation is probabilistically sophisticated if and only if it is subjective expected utility.
Subcalculus for set functions and cores of TU games.
Massimo Marinacci, Luigi Montrucchio
This paper introduces a subcalculus for general set functions and uses this framework to study the core of TU games. After stating a linearity theorem, we establish several theorems that characterize...
Random correspndences as bundles of random variables.
Adriana Castaldo, Massimo Marinacci
We prove results that relate random correspondences with their measurable selections, thus providing a foundation for viewing random correspondences as "bundles" of random variables.
A subjective spin on roulette wheels.
Paolo Ghirardato, Fabio Maccheroni, Massimo Marinacci, Marciano Siniscalchi
We provide a behavioral foundation to the notion of ‘mixture’ of acts, which is used to great advantage in he decision setting introduced by Anscombe and Aumann. Our construction allows one to...
Ambiguity from the Differential Viewpoint.
Paolo Ghirardato, Fabio Maccheroni, Massimo Marinacci
The objective of this paper is to show how ambiguity, and a decision maker (DM)'s response to it, can be modelled formally in the context of a very general decision model. In the first part of the...
The convexity-cone approach to comparative risk and downside risk.
Massimo Marinacci, Luigi Montrucchio
We establish a calculus characterization of the core of supermodular games, which reduces the description of the core to the computation of suitable Gateaux derivatives of the Choquet integrals...
Cores and stable sets of finite dimensional games.
Massimo Marinacci, Luigi Montrucchio
In this paper we study exact TU games having finite dimensional non-atomic cores, a class of games that includes relevant economic games. We first characterize them by showing that they are a...
Massimo Marinacci, Luigi Montrucchio
We study the properties of ultramodular functions, a class of functions that generalizes scalar convexity and that naturally arises in some economic and statistical applications.
Choquet insurance pricing: a caveat.
Erio Castagnoli, Fabio Maccheroni, Massimo Marinacci
We consider Choquet pricing functionals for insurance and financial markets. We show that when they depend on the distribution of the asset under a given probability measure, they reduce to standard...
Variational representation of preferences under ambiguity.
Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini
In the classic Anscombe and Aumann decision setting, we give necessary and sufficient conditions that guarantee the existence of a utility function u on outcomes and an ambiguity index c on the set...
Portfolio Selection with Monotone Mean-Variance Preferences.
Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini, Marco Taboga
We propose a portfolio selection model based on a class of preferences that coincide with mean-variance preferences on their domain of monotonicity, but differ where mean-variance preferences fail to...
On convexity and supermodularity.
Massimo Marinacci, Luigi Montrucchio
Concavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members...
Range Convexity and Ambiguity Averse Preferences
Ghirardato, Paolo, Marinacci, Massimo
We show that range convexity of beliefs, a 'technical' condition that appears naturally in axiomatizations of preferences in a Savage-like framework, imposes some unexpected restrictions when...
Coarse contingencies and ambiguity
Epstein, Larry G., Marinacci, Massimo, Seo, Kyoungwon
The paper considers an agent who must choose an action today under uncertainty about the consequence of any chosen action but without having in mind a complete list of all the contingencies that...
Revealed Ambiguity and Its Consequences: Updating
Paolo Ghirardato, Fabio Maccheroni, Massimo Marinacci
We study the updating of beliefs under ambiguity for invariant biseparable preferences. In particular, we show that a natural form of dynamic consistency characterizes the Bayesian updating of these...
Decomposition and Representation of Coalitional Games
A coalitional game is a real-valued set function v defined on an algebra F of subsets of a space X such that v(0)=0. We prove the existence of a one-to-one correspondence between coalitional games...
An Integral Representation for Non Simple Acts with Certainty Equivalents
In this paper we considera continuous subjective expected unity model with a connected space of consequences (CSEU, for brevity). This class of models has recently received attention (see Wakker...
On the Ranges of Baire and Borel Measures
Let X be a topological space, m a probability measure defined on the Baire s -field on X, and m ' a probability measure on teh Borel s -field which extends m. In the first part of the paper we deal...
Residual Measures and the Existence and Range of Probability Measures n Boolean Algebras
A Borel probability measure is residual if it gives measure zero to all meager subsets. We first give some existence results about this class of measures. Then they are applied in order to get some...
A Subjective Spin on Roulette Wheels
Paolo Ghirardato, Fabio Maccheroni, Massimo Marinacci, Marciano Siniscalchi
We provide a simple behavioral definition of 'subjective mixture' of acts for a large class of (not necessarily expected-utility) preferences. Subjective mixtures enjoy the same algebraic properties...
Ambiguity Aversion, Robustness, and the Variational Representation of Preferences
Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini
We characterize, in the Anscombe-Aumann framework, the preferences for which there are a utility functionu on outcomes and an ambiguity indexc on the set of probabilities on the states of the world...
Portfolio Selection with Monotone Mean-Variance Preferences
Massimo Marinacci, Fabio Maccheroni, Aldo Rustichini, Marco Taboga
We propose a portfolio selection model based on a class of preferences that coincide with mean-variance preferences on their domain of monotonicity, but differ where mean-variance preferences fail to...
Risk, ambiguity, and the separation of utility and beliefs.
Massimo Marinacci, Paolo Ghirardato
We introduce a general model of static choice under uncertainty, arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs. Most of the non-expected...
How to cut a pizza fairly: fair division with descreasing marginal evaluations.
Massimo Marinacci, Fabio Maccheroni
Existential and constructive solutions to the classic problems of fair division are known for individuals with constant marginal evaluations. By considering nonatomic concave capacities instead of...
Insurance Premia Consistent with the Market.
Erio Castagnoli, Fabio Maccheroni, Massimo Marinacci
We consider insurance prices in presence of an incomplete and competitive market. We show that if the insurance price system is internal, sublinear, and consistent with the market, then insurance...
Certainty Independence and the Separation of Utility and Beliefs.
Paolo Ghirardato, Fabio Maccheroni, Massimo Marinacci
Economists often operate under an implicit assumption that the tastes of a decision maker are constant, while his beliefs change with the availability of new information. It is therefore customary to...
A smooth model of decision making under ambiguity.
Peter Klibanoff, Massimo Marinacci, Sujoy Mukerji
We propose and axiomatize a new model of preferences that achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective information, and ambiguity...
Monotone Continuous Multiple Priors.
Massimo Marinacci, Fabio Maccheroni, Alain Chateauneuf, Jean-Marc Tallon
We show that the monotone continuity condition introduced by Villegas (1964) and Arrow (1970) is the behavioral counterpart of countable additivity (and relative weak compactness) in a multiple...
Larry G. Epstein, Massimo Marinacci
For non-atomic TU games nu satisfying suitable conditions, the core can be determined by computing appropriate derivatives of nu. Further, such computations yield one of two stark conclusions: either...
How to cut a pizza fairly: Fair division with decreasing marginal evaluations
Fabio Maccheroni, Fabio Maccheroni, Massimo Marinacci, Massimo Marinacci
Existential and constructive solutions to the classic problems of fair division are known for individuals with constant marginal evaluations. By considering nonatomic concave capacities instead of...
Paolo Ghirardato, Massimo Marinacci
We focus on the following uniqueness property of expected utility preferences: Agreement of two preferences on one interior indifference class implies their equality. We show that, besides expected...
Monotone continuous multiple priors
Alain Chateauneuf, Fabio Maccheroni, Massimo Marinacci, Jean-Marc Tallon
In a multiple priors model á la Gilboa and Schmeidler (1989), we provide necessary and sufficient behavioral conditions ensuring the countable additivity and non-atomicity of all priors. Copyright...
Portfolio Selection with Monotone Mean-Variance Preferences
Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini, Marco Taboga
We propose a portfolio selection model based on a class of monotone preferences that coincide with mean-variance preferences on their domain of monotonicity, but differ where mean-variance...
Uncertainty Averse Preferences
Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci, Luigi Montrucchio
We study uncertainty averse preferences, that is, complete and transitive preferences that are convex and monotone. We establish a representation result, which is at same time general and rich in...
Monotone continuous multiple priors
Alain Chateauneuf, Fabio Macheronni, Massimo Marinacci, Jean-Marc Tallon
We show that the monotone continuity condition introduced by Arrow (1970) is the behavioral counterpart of countable additivity and weak compactness of the set of priors in a maxmin expected utility...
Monotone continuous multiple priors
Alain Chateauneuf, Fabio Macheronni, Massimo Marinacci, Jean-Marc Tallon
We show that the monotone continuity condition introduced by Arrow (1970) is the behavioral counterpart of countable additivity and weak compactness of the set of priors in a maxmin expected utility...
Finitely Additive and Epsilon Nash Equilibria
We prove the existence of a mixed strategy Nash equilibrium in normal form games when the space of mixed strategies consists of finitely additive probability measures. It is then proved that from...
A uniqueness theorem for convex-ranged probabilities
A finitely additive probability measure P defined on a class of subsets of a space is convex-ranged if, for all P(A)>0 and all 0 < < 1, there exists a set, ∋ B⊆A, such that P(B)= P(A).Our main...
Objective and Subjective Rationality
Itzhak Gilboa, Fabio Maccheroni, Massimo Marinacci, David Schmeidler
On the Computation of Optimal Monotone Mean-Variance Portfolios via Truncated Quadratic Utility
Ales Cerný, Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini
We report a surprising link between optimal portfolios generated by a special type of variational preferences called divergence preferences (cf. [8]) and optimal portfolios generated by classical...
Complete Monotone Quasiconcave Duality
Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci, Luigi Montrucchio
We introduce a notion of complete monotone quasiconcave duality and we show that it holds for important classes of quasiconcave functions.
Monotone continuous multiple priors
Alain Chateauneuf, Fabio Macheronni, Massimo Marinacci, Jean-Marc Tallon
We show that the monotone continuity condition introduced by Arrow (1970) is the behavioral counterpart of countable additivity and weak compactness of the set of priors in a maxmin expected utility...
Risk Measures: Rationality and Diversification
Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci, Luigi Montrucchio
When there is uncertainty about interest rates (typically due to either illiquidity or defaultability of zero coupon bonds) the cash- additivity assumption on risk measures becomes problematic. When...
Risk Measures: Rationality and Diversification
Simone Cerreia-Vioglio, Fabio Maccheroni, Massimo Marinacci, Luigi Montrucchio
When there is uncertainty about interest rates (typically due to either illiquidity or defaultability of zero coupon bonds) the cash- additivity assumption on risk measures becomes problematic. When...
PORTFOLIO SELECTION WITH MONOTONE MEAN-VARIANCE PREFERENCES
Fabio Maccheroni, Massimo Marinacci, Aldo Rustichini, Marco Taboga
Recursive smooth ambiguity preferences
Klibanoff, Peter, Marinacci, Massimo, Mukerji, Sujoy
This paper axiomatizes an intertemporal version of the Smooth Ambiguity decision model developed in [P. Klibanoff, M. Marinacci, S. Mukerji, A smooth model of decision making under ambiguity,...
On the Smooth Ambiguity Model: A Reply
Peter Klibanoff, Massimo Marinacci, Sujoy Mukerji
Epstein (2009) describes three Ellsberg-style thought experiments and argues that they pose difficulties for the smooth ambiguity model of decision making under uncertainty developed by Klibanoff,...