Institute of Information Theory and Automation

Publication details

Sparse robust portfolio optimization via NLP regularizations

Research Report

Branda Martin, Červinka Michal, Schwartz A.


publisher: ÚTIA AV ČR v. v. i., (Praha 2016)

edition: Research Report 2358

project(s): GA13-01930S, GA ČR, GA15-00735S, GA ČR

keywords: Conditional Value-at-Risk, Value-at-Risk, risk measure

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abstract (eng):

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.

abstract (eng):

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

RIV: BB

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Institute of Information Theory and Automation