In this talk I will present two applications of convex optimization.
First, I will introduce you to the Kelly strategy. Kelly strategy is to maximize long run wealth of the investor by maximizing the expected logarithmic utility of wealth. It is called the "Fortune’s formula” by Edward Thorp. Kelly strategy dominant all other strategies in the long run but can also lead to considerable losses a small percent of the time.
Second, to avoid large losses in worst cases, I will introduce the distributional robust Kelly strategy. Then I will show concretely how to transform the distributional robust problems to tractable convex optimization problems for a large class of uncertainty sets, and demonstrate its performance for horse betting games.