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An incremental bundle method for portfolio selection problem under second-order stochastic dominance

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Abstract

In this paper, we propose an incremental bundle method with inexact oracle for solving the portfolio optimization with stochastic second-order dominance (SSD) constraints. We first relax the SSD problem as a stochastic semi-infinite programming (SIP) problem. For the particular case of SIP problem, we exploit the improvement function and the idea of incremental technique for dealing with the infinitely many constraints. In the stochastic model, as an adding-rules, the “inexact oracle” is introduced in this algorithm. Therefore, the algorithm does not need all the information about the constraints, but only needs the inexact information of one component function to update the bundle and produces the search direction. Our numerical results on solving the academic problems have shown advantages of the incremental bundle method over three existing algorithms. Finally, numerical results on a part of portfolio optimization problem are presented by using the FTSE100 Index.

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Funding

This work was supported by the National Natural Science Foundation of China (Nos. 11801503, 11701061) Zhejiang Provincial Natural Science Foundation of China (No. LY20A 010025) and the Natural Science Foundation of ShanDong (No. ZR2019BA014).

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Authors and Affiliations

  1. School of Finance, Zhejiang University of Finance and Economics, Hangzhou, 310018, China

    Jian Lv

  2. Dalian University of Technology, Dalian, 116024, China

    Ze-Hao Xiao & Li-Ping Pang

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  1. Jian Lv
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  2. Ze-Hao Xiao
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  3. Li-Ping Pang
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Correspondence to Li-Ping Pang.

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Lv, J., Xiao, ZH. & Pang, LP. An incremental bundle method for portfolio selection problem under second-order stochastic dominance. Numer Algor 85, 653–681 (2020). https://doi.org/10.1007/s11075-019-00831-6

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