bv_cvxbook_extra_exercises

# the revenue from selling the products is pt s where

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Unformatted text preview: vector p in the second condition, so that 1T p = 1, we can interpret it as a probability vector on the outcomes. The condition RT p = 0 means that E Rx = pT Rx = 0 for all x, i.e., the expected return is zero for all betting strategies. In economics, p is called a risk neutral probability. We can therefore rephrase the arbitrage theorem as follows: There is no sure-win betting strategy (or arbitrage opportunity) if and only if there is a probability vector on the outcomes that makes all bets fair (i.e., the expected gain is zero). (b) Betting. In a simple application, we have exactly as many wagers as there are outcomes (n = m). Wager i is to bet that the outcome will be i. The returns are usually expressed as odds. For example, suppose that a bookmaker accepts bets on the result of the 2000 European soccer championships. If the odds against Belgium winning are 14 to one, and we bet \$100 on Belgium, then we win \$1400 if they win the tournament, and we lose \$100 otherwise. In general, if we have m possible outcomes, and the odds against outcome...
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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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