lecture8-2k

# lecture8-2k - AEB 6182 Lecture VIII Professor Charles Moss...

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AEB 6182 Lecture VIII Professor Charles Moss 1 Overview of Stochastic Dominance Lecture VIII I. Expected Utility Versus Risk Efficiency A. In this course, we started with the precept that individual’s choose between actions or alternatives in a way that maximizes their expected utility. Axiomatically, this assumption is based on Bernoulli’s principle which was expanded upon by Von Neumann and Morgenstern. Mathematically, this principle is based on three axioms (Anderson, Dillon, and Hardaker p 66-69): 1. Ordering and transitivity: A person either prefers one of two risky prospects a 1 and a 2 or is indifferent between them. Further if the individual prefers a 1 to a 2 and a 2 to a 3 , then he prefers a 1 to a 3 . 2. Continuity. If a person prefers a 1 to a 2 to a 3 , then there exists some subjective probability level p[a 1 ] such that he is indifferent between the gamble paying a 1 with probability p[a 1 ] and a 3 with probability 1-p[a 3 ] which leaves him indifferent with a 2 . 3. Independence. If a 1 is preferred to a 2 , and a 3 is any other risky prospect, a lottery with a 1 and a 3 outcomes will be preferred to a lottery with a 2 and a 3 outcomes when p[a 1 ]=p[a 2 ]. In other words, preference between a 1 and a 2 is independent of a 3 . B. However, some literature has raised questions regarding the adequacy of these assumptions: 1. Allais (1953) raised questions about the axiom of independence. 2. May (1954) and Tversky (1969) questioned the transitivity of preferences. C. These studies question whether preferences under uncertainty are adequately described by the traditional expected utility framework. One alternative is to develop risk efficiency criteria rather than expected utility axioms. 1. Risk efficiency criteria are an attempt to reduce the collection of all possible alternatives to a smaller collection of risky alternatives that contain the optimum choice. 2. One example was the mean-variance derivation of optimum portfolios. a. The EV frontier contained the set of possible portfolios such that no other portfolio could be constructed with a higher return with the same risk measured as the variance of the portfolio. b.

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lecture8-2k - AEB 6182 Lecture VIII Professor Charles Moss...

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