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 6669):
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 1p[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 meanvariance 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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 Moss
 Utility, stochastic dominance, degree stochastic dominance, Professor Charles Moss II

Click to edit the document details