### A Free Lunch on Wall Street

Hi,

In order to while away some time in the last few days, I managed to work out a proof that for any time interval where there are 2 markets trading identical assets, there is an arbitrage opportunity in a given time window, where the price is sampled at discrete intervals within that time window.

Generally, when speaking of arbitrage, people do not really talk about the time horizon or the time dimension in which the arbitrage opportunity would disappear. For any time interval where there will definitely be arbitrage opportunities if there is no transportation cost. But if such costs are introduced, the probability of having an arbitrage opportunity can be worked out.

Arbitrage without a time dimension Zeno’s paradox to me at this point of time.

The proof is more intuitive than mathematically rigorous.

I got my personal diary pagers scanned where I made the entry. Can you be good enough to have a look at it and comment? I am wondering whether any body else also has come up with such an argument?

(c) 2008, Suminda Sirinath Salpitikorala Dharmasena, All rights reserved.

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