Title: Solving the value-at-risk minimisation model with linear programming techniques

Authors: Chunhui Xu; Xiaolin Huang; Yanli Huo; Shuning Wang

Addresses: Department of Risk Science in Finance and Management, Faculty of Social Systems Science, Chiba Institute of Technology, Chiba 275-0016, Japan ' Department of Automation, Tsinghua University, Beijing, 100084, China ' College of Economics and Management, China Jiliang University, Hangzhou, Zhejiang 310018, China ' Department of Automation, Tsinghua University, Beijing, 100084, China

Abstract: This study considers portfolio selection problems in which risk is measured using value-at-risk (VaR). Because VaR is generally a non-convex and non-smooth function, conventional optimisation methods fail to solve portfolio selection models based on VaR. This has been considered an open problem since the 1990s. The study first proves that VaR is a continuous piecewise linear function of position when it is estimated with the scenario simulation method, and then, proposes a method for solving VaR minimisation models. The proposed method can yield a good local minimum or even a global optimum, although it has no theoretical guarantee. Because the proposed method uses only linear programming techniques, common linear programming solution software can be employed to solve VaR minimisation models of practical sizes in a short period of time. To illustrate the performance of the proposed method, we use it to solve a VaR minimisation model with 30 equities and 1,000 scenarios. We also compare the precision and computing time with another method. The results show that both methods can yield the optimal solution, but the proposed method is much faster.

Keywords: portfolio selection; risk measurement; value-at-risk; VaR minimisation; optimisation; linear programming; scenario simulation.

DOI: 10.1504/AJMSA.2016.080470

Asian Journal of Management Science and Applications, 2016 Vol.2 No.3, pp.228 - 244

Received: 23 Jul 2015
Accepted: 03 Nov 2015

Published online: 25 Nov 2016 *

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