EURO 2024 Copenhagen
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3465. Nonsmooth optimization in sparse portfolio selection

Invited abstract in session TB-32: Nonsmooth optimization and applications, Part II, stream Advances in large scale nonlinear optimization.

Tuesday, 10:30-12:00
Room: 41 (building: 303A)

Authors (first author is the speaker)

1. Zelda Marino
University of Naples Parthenope
2. Stefania Corsaro
University of Naples Parthenope
3. Valentina De Simone
Mathematics and Physics, University of Campania "L. Vanvitelli"

Abstract

In this talk we describe a fused lasso approach for the regularized multi-period mean variance model, in a Markowitz framework. Multi-period portfolio selection aims at computing the optimal allocation of wealth among n assets within a time horizon of m periods. In addition, the investor can rebalance the portfolio at the beginning of each period. We define a multi-period minimum variance model with final expected return and introduce l1-regularization techniques to stabilize the solution process, which is well-known to be ill-conditioned because of assets correlation. Two l1-penalty terms are used: one on portfolio weights promotes sparsity in the solution; this allows investor to reduce both the number of positions to be monitored and the transaction costs. A second l1-penalty term is added to the objective function of the arising optimization problem. This is a penalization on the portfolio turnover, thus it limits the number of transactions by preserving the pattern of active positions. The model leads to a nonsmooth constrained optimization problem, where the inequality constraints are aimed to guarantee at least a minimum level of expected wealth at each date. We develop iterative algorithms based on first order methods. We validate the approach showing results of tests performed on real data.

Keywords

Status: accepted

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