I started by recapitulating the ¡­

I started by recapitulating the basic quantities underlying a single-period market. I then introduced the notion of a linear pricing measure, collected some properties of such measures, and proved that the existence of linear pricing measures are equivalent to the absence of dominant trading strategies. As part of this, I spent some time on linear programming problems and recalled a few key facts from duality theory.

Exercises for Tuesday Sep 1: From the book, Exercises 1.1, 1.2, 1.3, 1.4, 1.5. Regarding Exercises 1.4 and 1.5, they involve the use of "arbitrage" and the "law of one price", which we have not yet covered in detail, so you have to read about it in the book. In addition to the above exercises, you should prove the following statement "the absence of dominant trading strategies implies the existence of a linear pricing measure" (the implication that we did not have time to complete in today's lecture).