uncle arbitrageur

"if the internally generated arbitrage profits are large enough to compensate for the information disadvantage faced by the market maker."
along these lines
consider uncle sam
given  his limitless dollar mine
 as market maker
does MM playing MM gain max still hold ?
does uncle need or benefit from a budget constraint ?
"if the internally generated arbitrage profits are large enough to compensate for the information disadvantage faced by the market maker."

rajiv sethi


"Suppose that there were only two Oscar categories (Best Picture and Best Director) and consider the following seven events:

1. Lincoln to win Best Picture
2. Lincoln not to win Best Picture
3. Lincoln to win Best Director
4. Lincoln not to win Best Director
5. Lincoln to win 0 Oscars
6. Lincoln to win 1 Oscar
7. Lincoln to win 2 Oscars

Let p_i denote the price of contract i, where i = 1,...,7, where each contract pays out one dollar if the event in question occurs. Clearly we must have

p₁ + p₂ = p₃ + p₄ = 1,

otherwise there would be an arbitrage opportunity. Similarly, we must have

p₅ + p₆ + p₇ = 1.

Price adjustments in response to orders are such that these equalities are continuously maintained. Somewhat less obviously, we must also have

p₁ + p₃ = p₆ + 2p₇.

If this condition were violated, then one could construct a portfolio that guaranteed a positive profit no matter what the eventual outcome may be. To see this, suppose that prices were such that

p₁ + p₃ > p₆ + 2p₇.

In this case, the following portfolio would yield a risk-free profit: buy one unit each of contracts 2, 4, and 6, and two units of contract 7. This would cost

(1 - p₁) + (1 - p₃) + p₆ + 2p₇ < 2.

The payoff from this portfolio would be exactly 2, no matter how things turn out. If Lincoln wins no Oscars then contracts 2 and 4 each pay out one unit, if it wins one Oscar then contract 6 pays out a unit, in addition to either contract 2 or contract 4, and if it wins two Oscars then each of the two units of contract 7 pays out. "