/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Impatti, adattamento e vulnerabilita Le cause e le responsabilita dei cambiamenti climatici sono state trattate sul numero di ottobre della rivista Cda. Approfondiamo l’argomento presentando il documento: “Cambiamenti climatici 2007: impatti, adattamento e vulnerabilita” votato ad aprile 2007 dal secondo gruppo di lavoro del Comitato Intergovernativo sui Cambiamenti Climatici (Intergovernmental Panel on Climate Change). Si tratta del secondo di tre documenti che compongono il quarto rapporto sui cambiamenti climatici.

/pdf/climate-change-2007-impacts-adaptation-and-vulnerability-31xc1cf4d3.pdf

Climate Change 2007: Impacts, Adaptation and Vulnerability.

Information Theory and Reliable Communication

The theory of precautionary saving is shown in this paper to be isomorphic to the Arrow-Pratt theory of risk aversion, making possible the application of a large body of knowledge about risk aversion to precautionary saving, and more generally, to the theory of optimal choice under risk In particular, a measure of the strength of precautionary saving motive analogous to the Arrow-Pratt measure of risk aversion is used to establish a number of new propositions about precautionary saving, and to give a new interpretation of the Oreze-Modigliani substitution effect

Precautionary Saving in the Small and in the Large

We propose and axiomatize a model of preferences over acts such that the decision maker evaluates acts according to the expectation (over a set of probability measures) of an increasing transformation of an act's expected utility. This expectation is calculated using a subjective probability over the set of probability measures that the decision maker thinks are relevant given her subjective information. A key feature of our model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective information, and ambiguity attitude, a characteristic of the decision maker's tastes. We show that attitudes towards risk are characterized by the shape of the von Neumann-Morgenstern utility function, as usual, while attitudes towards ambiguity are characterized by the shape of the increasing transformation applied to expected utilities. We show that the negative exponential form of this transformation is the special case of constant ambiguity aversion. Ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures. This characterization of ambiguity is formally related to the definitions of subjective ambiguity advanced by Epstein-Zhang (2001) and Ghirardato-Marinacci (2002). One advantage of this model is that the well-developed machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes. The model is also distinct from many in the literature on ambiguity in that it allows smooth, rather than kinked, indifference curves. This leads to different behavior and improved tractability, while still sharing the main features (e.g., Ellsberg's Paradox, etc.). The Maxmin EU model (e.g., Gilboa and Schmeidler (1989)) with a given set of measures may be seen as an extreme case of our model with infinite ambiguity aversion. Two illustrative applications to portfolio choice are offered.

/pdf/a-smooth-model-of-decision-making-under-ambiguity-2qvm7ggyao.pdf

A Smooth Model of Decision Making under Ambiguity

We propose and axiomatize 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 operator, u is a vN-M utility function, φ is an increasing transformation,
and μ is a subjective probability over the set Π of probability measures π that the
decision maker thinks are relevant given his subjective information. A key feature of our
model is that it achieves a separation between ambiguity, identified as a characteristic
of the decision maker’s subjective information, and ambiguity attitude, a characteristic
of the decision maker’s tastes. We show that attitudes towards risk are characterized
by the shape of u, as usual, while attitudes towards ambiguity are characterized by the
shape of φ. We also derive φ (x) = −1
α
e−αx as the special case of constant ambiguity
aversion. Ambiguity itself is defined behaviorally and is shown to be characterized by
properties of the subjective set of measures Π. This characterization of ambiguity is
formally related to the definitions of subjective ambiguity advanced by Epstein-Zhang
(2001) and Ghirardato-Marinacci (2002). One advantage of this model is that the welldeveloped
machinery for dealing with risk attitudes can be applied as well to ambiguity
attitudes. The model is also distinct from many in the literature on ambiguity in that
allows smooth, rather than kinked, indifference curves. This leads to different behavior
and improved tractability, while still sharing the main features (e.g., Ellsberg’s Paradox,
etc.). The Maxmin EU model (e.g., Gilboa and Schmeidler (1989)) with a given set of
measures may be seen as an extreme case of our model with infinite ambiguity aversion.
Two illustrative applications to portfolio choice are offered.

/pdf/a-smooth-model-of-decision-making-under-ambiguity-yoi825dq9u.pdf

A Smooth Model of Decision Making Under Ambiguity

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 such that, for all acts f and g,

.

The function u represents the decision maker's risk attitudes, while the index c captures his ambiguity attitudes. These preferences include the multiple priors preferences of Gilboa and Schmeidler and the multiplier preferences of Hansen and Sargent. This provides a rigorous decision-theoretic foundation for the latter model, which has been widely used in macroeconomics and finance.

/pdf/ambiguity-aversion-robustness-and-the-variational-zvmaigz0wj.pdf

Ambiguity Aversion, Robustness, and the Variational Representation of Preferences

http://static.luiss.it/hey/ambiguity/papers/Ghirardato_Maccheroni_Marinacci_2004.pdf

Massimo Marinacci

Papers

A Smooth Model of Decision Making under Ambiguity

A Smooth Model of Decision Making Under Ambiguity

Ambiguity Aversion, Robustness, and the Variational Representation of Preferences

Differentiating ambiguity and ambiguity attitude

Ambiguity Made Precise: A Comparative Foundation