TY - JOUR
T1 - A Krasnoselskii-Mann Proximity Algorithm for Markowitz Portfolios with Adaptive Expected Return Level
AU - Lin , Yizun
AU - He , Yongxin
AU - Lai , Zhao-Rong
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 113
EP - 138
PY - 2024
DA - 2024/11
SN - 22
DO - http://doi.org/10.4208/ijnam2025-1006
UR - https://global-sci.org/intro/article_detail/ijnam/23569.html
KW - Markowitz portfolio, adaptive expected return, $ℓ^1$ regularization, Krasnoselskii-Mann algorithm.
AB - <p style="text-align: justify;">Markowitz’s criterion aims to balance expected return and risk when optimizing the
portfolio. The expected return level is usually fixed according to the risk appetite of an investor,
then the risk is minimized at this fixed return level. However, the investor may not know which
return level is suitable for her/him and the current financial circumstance. It motivates us to
find a novel approach that adaptively optimizes this return level and the portfolio at the same
time. It not only relieves the trouble of deciding the return level during an investment but also
gets more adaptive to the ever-changing financial market than a subjective return level. In order
to solve the new model, we propose an exact, convergent, and efficient Krasnoselskii-Mann Proximity Algorithm based on the proximity operator and Krasnoselskii-Mann momentum technique.
Extensive experiments show that the proposed method achieves significant improvements over
state-of-the-art methods in portfolio optimization. This finding may contribute a new perspective
on the relationship between return and risk in portfolio optimization</p>