Today I continued with optimal ¡­

Today I continued with optimal portfolio problems (maximizing expected utility of terminal wealth), highlighting two approaches for solving such problems: 1. The direct approach in which optimization is done with respect to the trading strategies H and for which the first order conditions at a maximum provide the relevant (nonlinear) equations to determine the optimal H. 2. The in-direct (risk-neutral probability) approach in which the problem is decomposed into two separate optimization problems. In the first problem the optimal terminal wealth is determined. Given the optimal terminal wealth, we then in the second problem determine the trading strategy that generates this wealth. Continuing with optimization problems, I introduced the the so-called consumption-investment problem in which the goal is to maximize expected utility from consumption. Similarly, two approaches for solving this optimization problem were outlined.

Exercises (for Tuesday next week): 1.19, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7

Next week I will be out traveling and Bernt ?ksendal will step in for me.