Risk Attitudes and Measures of Value for Risky Lotteries

Abstract

The topic of this thesis is decision-making under risk. I focus my analysis on expected utility theory by von Neumann and Morgenstern. I am especially interested in modeling risk attitudes represented by Bernoulli utility functions that belong to the following classes: Constant Absolute Risk Aversion, Decreasing Absolute Risk Aversion (understood as strictly decreasing) and in particular a subset thereof - Constant Relative Risk Aversion. I build a theory of buying and selling price for a lottery, the concepts defined by Raiffa, since such theory proves useful in analyzing a number of interesting issues pertaining to risk attitudes' characteristics within expected utility model. In particular, I analyze the following: - Chapter 2 - expected utility without consequentialism, buying/selling price gap, preference reversal, Rabin paradox - Chapter 3 - characterization results for CARA, DARA, CRRA, simple strategies and an extension of Pratt result on comparative risk aversion - Chapter 4 - riskiness measure and its intuition, extended riskiness measure and its existence, uniqueness and properties