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\title{Diversity and relative arbitrage in equity markets}
\author{Konstantinos Kardaras\\
  Columbia University} \date{Computational Finance Seminar, October
  14, 5:30, PPB 300}

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A financial market is called "diverse" if no single stock is ever
allowed to dominate the entire market in terms of relative
capitalization. In the context of the standard Ito-process model
initiated by Samuelson (1965) we formulate this property (and the
allied, successively weaker notions of "weak diversity" and
"asymptotic weak diversity") in precise terms. We show that diversity
is possible to achieve, but delicate. Several illustrative examples
are provided, which demonstrate that weakly-diverse financial markets
contain relative arbitrage opportunities: it is possible to outperform
(or underperform) such markets over sufficiently long time-horizons,
and to underperform them significantly over arbitrary time-horizons.
The existence of such relative arbitrage does not interfere with the
development of option pricing, and has interesting consequences for
the pricing of long-term warrants and for put-call parity. Several
open questions are suggested for further study.

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