The Arbitrage Theorem
Abstract
The theory of arbitrage is one of the cornerstones of the theory
of portfolio choice and asset pricing. It is a basic constraint
necessary for many theories in financial economics. In layman’s
terms, an arbitrage opportunity is a “free-lunch,” but more
technically, it is when one takes simultaneous positions in
different assets so that one is guaranteed a riskless profit
higher than the riskless return. The general interest in
arbitrage-free prices is that the most important conclusions
of market economics can only be made under the condition of
no-arbitrage. Furthermore, the price of a security is considered
fair if there is no arbitrage opportunity at that price.
The Arbitrage theorem exists in a probability-theoretic setting,
in which there are outcomes with associated probabilities and
wagers and bets. The theorem tells us that either there is a set
of risk-neutral probabilities such that the expected value of
each wager is equal to zero, or else there exists a betting
strategy that leads to a sure win.
Table of Contents
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