Portfolio optimization with discrete constraints

[rluce]

Why this Nup?
Many practical aspects of asset allocation are of discrete nature: Minimum buy-in, maximum number of allowed trades per period, market segmentation, etc.

Does it fall under an existing category?

• Other: finance

What will the API be?

asset_allocs = nupstup.portfolio_optimization(
    factor_matrix=H  # H.T@H is the variance-covariance matrix
    covariance=Sigma  # Sigma is the variance-covariance matrix
    mu=mu  # estimated first moments of return function
    maxnum_transactions=20  # No more than 20 trades
    maxnum_allocations=50  # No more than 50 allocations at a time (e.g., online problem)
    min_invest_long=0.05  # For long allocations, need at least 5% of total investment
    min_invest_short=0.01  # For short allocations, need at least 1% of total investment
    max_total_short=0.1  # Maximum 10% short selling
    [...]

Here the objective function would be min x.T @ H.T @ H @ x - mu @ x

Note that we focus here on the model

min x.T @ H.T @ H @ x - mu @ x
s.t. something

and another NUP should cover the model

max  mu @ x
s.t. something
    x.T @ H.T @ H @ x <= omega^2

Both Nups can share most code and documentation.

Other random thoughts:

• Allow entropy weights through https://github.compute.gurobi.com/Gurobi/Gurobi/issues/5671#issuecomment-38316
• Can we incorporate an online variation of this portfolio model by accepting a vector of existing allocations?
• Should we incorporate market segmentation data?
• Use numpy/pandas as input structures to provide input data to the Nup?