Sparse robust portfolio optimization via NLP regularizations

0468834 - ÚTIA 2017 CZ eng V - Research Report
Branda, Martin - Červinka, Michal - Schwartz, A.
Sparse robust portfolio optimization via NLP regularizations.
Praha: ÚTIA AV ČR v. v. i., 2016. 19 s. Research Report, 2358.
R&D Projects: GA ČR GA15-00735S
Grant - others:GA ČR(CZ) GA13-01930S
Institutional support: RVO:67985556
Keywords : Conditional Value-at-Risk * Value-at-Risk * risk measure
Subject RIV: BB - Applied Statistics, Operational Research
http://library.utia.cas.cz/separaty/2016/E/branda-0468834.pdf

We deal with investment problems where we minimize a risk measure under a condition on the sparsity of the portfolio. Various risk measures are considered including Value-at-Risk and Conditional Value-at-Risk under normal distribution of returns and their robust counterparts are derived under moment conditions, all leading to nonconvex objective functions. We propose four solution approaches: a mixed-integer formulation, a relaxation of an alternative mixed-integer reformulation and two NLP regularizations. In a numerical study, we compare their computational performance on a large number of simulated instances taken from the literature.

We deal with investment problems where we minimize a risk measure
under a condition on the sparsity of the portfolio. Various risk measures
are considered including Value-at-Risk and Conditional Value-at-Risk
under normal distribution of returns and their robust counterparts are
derived under moment conditions, all leading to nonconvex objective
functions. We propose four solution approaches: a mixed-integer formulation,
a relaxation of an alternative mixed-integer reformulation and
two NLP regularizations. In a numerical study, we compare their computational
performance on a large number of simulated instances taken
from the literature.
Permanent Link: http://hdl.handle.net/11104/0266849