Today I introduced the notion ¡­

Today I introduced the notion of complete markets and showed that a marked is complete iff the number assets available for investment (bank + securities) equals the number of "states of the world" (the "amount of randomness"). This result was illustrated by a few examples. Next, we proved that a contingent claim is attainable iff the Q-expected discounted payoff EQ[X/B1] is constant with respect to the risk-netural probability measure Q. The proof involved the use of Farkas' lemma (cf. Exercise 1.11). We concluded by showing that the market is complete iff the set M of risk-netural probability measures is a singleton, i.e., consists of only one element.

Tuesday and Thursday next week will be devoted to lectures.

Finally, I am attaching some notes (written by Geir Dahl) on linear programming and its applications to the "arbitrage" theorem and the "dominant trading strategies" theorem. You can read these notes as a supplement to the book. Linear programming theory is utilized several places in the book and as such provides an important tool to us!