I'm new to finance in general, and recently read about Modern Portfolio Theory. Now I'm wondering how to add the following constraint on asset weights:
- Each asset weight $w_i$ should either be $w_i = 0$, or it should be $0.05 <= w_i <= 1.0$
(With 0.05 as the lower bound just being an example.)
From doodling a bit, it looks to me as if that would give a non-convex problem, and thus the usual optimization approaches won't work.
Can someone point me into the right direction on how to efficiently solve this problem for a large number of assets?
Edit: Alternatively, I could reformulate the additional constraint as
- For each asset weight $0.05 <= w_i <= 1.0$
- For each asset there is an indicator $I_i \in {0, 1}$
- The combined weight of the selected assets must be 1: $\sum I_i w_i = 1$
What optimization technique is suitable for this problem?