optimal sparse portfolios in continuous time

We discuss sparse portfolio optimization in continuous time.

Optimization objective is to maximize an expected utility as in the

classical Merton problem but with regularizing sparsity constraints.

Such constraints aim for asset allocations that contain only few assets or

that deviate only in few coordinates from a reference benchmark allocation.

With a focus on growth optimization, we show empirical results for various

portfolio selection strategies with and without sparsity constraints,

investigating different portfolios of stock indicies, several performance

measures and adaptive methods to select the regularization parameter.

Sparse optimal portfolios are less sensitive to estimation

errors and performance is superior to portfolios without sparsity

constraints in reality, where estimation risk and model uncertainty must

not be ignored.