The topic today was portfolio ¡­

The topic today was portfolio optimization in incomplete markets. I outlined two approaches for solving such problems. The first one was a natural extension of "risk-netural probability" approach utilized several times before for complete markets, where the main new aspect amounted to a proper characterization of the set of attainable claims. The second approach was based on enlarging the market with enough "artificial" risky assets to make the resulting market complete, and then perform optimization in this enlarged market with the constraint that investment in the added artificial asset was not allowed, thereby replacing the original problem in a incomplete market with an optimization problem in a complete market with an additional constraint. To solve this constrained optimization problem one can effectively use the approach introduced last week for problems with short sales restrictions (Section 2.5).

I have decided to drop Section 2.7 (equilibrium models) from the syllabus. On Thursday I will begin with Chapter 3 (multi-period markets).