Choice under Risk and Uncertainty

Magister Ludi

Contents

(1) General Introduction
(A) Randomness in Economic Theory
(B) Risk, Uncertainty and Expected Utility

(2) The Expected Utility Hypothesis
(A) Bernoulli and the St. Petersburg Paradox
(B) The von Neumann-Morgenstern Expected Utility Theory
(i) Lotteries
(ii) Axioms of Preference
(iii) The von Neumann-Morgenstern Utility Function
(iv) Expected Utility Representation
(C) The Early Debates
(i) Cardinality
(ii) The Independence Axiom
(iii) Allais's Paradox and the "Fanning Out" Hypothesis
(D) Alternative Expected Utility
(i) Weighted Expected Utility
(ii) Non-Linear Expected Utility
(iii) Preference Reversals and Regret Theory

(3) Subjective Expected Utility
(A) The Concept of Subjective Probability
(B) Savage's Axiomatization
(C) The Anscombe-Aumann Approach
(D) The Ellsberg Paradox and State-Dependent Preferences

(4) The State-Preference Approach
(A) State-Contingent Markets
(B) The Individual Optimum
(C) Yaari Characterization of Risk-Aversion
(D) Application: Insurance

(5) The Theory of Risk Aversion
(A) Expected Utility with Univariate Payoffs
(B) Risk Aversion, Neutrality and Proclivity
(C) Arrow-Pratt Measures of Risk-Aversion
(D) Application: Portfolio Allocation and Arrow's Hypothesis
(E) Ross's Stronger Risk-Aversion Measurement

(6) Riskiness
(A) First and Second Order Stochastic Dominance
(B) The Characterization of Increasing Risk
(C) Application: Portfolio Allocation
(D) Alternative Measures of Increasing Risk

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