Is there a way to phrase the following problem as an effective convex optimization problem ?
There are 2 baskets of stocks, A and B, and every day we need to pick what proportion we are going to buy from either basket. For example, on a particular day we might allocate all the money in basket A, on another day we might buy 0.5 of A and 0.5 of B. Our choice of what proportion to assign should be based on a function of indicators that convey information about each basket. Indicators for example might be how the basket has been doing recently or how the basket is doing compared to the other basket.
A simple way (but indirect) to set this up as a convex problem would be to phrase it as a logistic regression problem. For each day, we predict which basket will perform better based on a linear combination of the indicators. The result is a logit (0-1 sigmoid, for the A-B baskets) function on the indicators that estimates the probability of a basket outperforming the other. We can then use this probability estimate as the proportion to allocate to each basket. However, this is an indirect method and fails to really optimize for profit. Can you think of another formulation which is efficiently solvable and is phrased in terms of profit?
