Research article
Special Issues
An intrinsic robust rankoneapproximation approach for currency portfolio optimization

1.
Department of Industrial Engineering, Tsinghua University, Beijing 100084, P.R. China

2.
Department of Statistics, University of Wisconsin at Madison, Madison, WI 53706, USA

Received:
31 August 2017
Accepted:
19 January 2018
Published:
13 March 2018


JEL Codes:
G11


A currency portfolio is a special kind of wealth whose value fluctuates with foreign exchange rates over time, which possesses 3Vs (volume, variety and velocity) properties of big data in the currency market. In this paper, an intrinsic robust rank one approximation (ROA) approach is proposed to maximize the value of currency portfolios over time. The main results of the paper include four parts: Firstly, under the assumptions about the currency market, the currency portfolio optimization problem is formulated as the basic model, in which there are two types of variables describing currency amounts in portfolios and the amount of each currency exchanged into another, respectively. Secondly, the rank one approximation problem and its variants are also formulated to approximate a foreign exchange rate matrix, whose performance is measured by the Frobenius norm or the 2norm of a residual matrix. The intrinsic robustness of the rank one approximation is proved together with summarizing properties of the basic ROA problem and designing a modified power method to search for the virtual exchange rates hidden in a foreign exchange rate matrix. Thirdly, a technique for decision variables reduction is presented to attack the currency portfolio optimization. The reduced formulation is referred to as the ROA model, which keeps only variables describing currency amounts in portfolios. The optimal solution to the ROA model also induces a feasible solution to the basic model of the currency portfolio problem by integrating forex operations from the ROA model with practical forex rates. Finally, numerical examples are presented to verify the feasibility and e ciency of the intrinsic robust rank one approximation approach. They also indicate that there exists an objective measure for evaluating and optimizing currency portfolios over time, which is related to the virtual standard currency and independent of any real currency selected specially for measurement.
Citation: Hongxuan Huang, Zhengjun Zhang. An intrinsic robust rankoneapproximation approach for currency portfolio optimization[J]. Quantitative Finance and Economics, 2018, 2(1): 160189. doi: 10.3934/QFE.2018.1.160

Abstract
A currency portfolio is a special kind of wealth whose value fluctuates with foreign exchange rates over time, which possesses 3Vs (volume, variety and velocity) properties of big data in the currency market. In this paper, an intrinsic robust rank one approximation (ROA) approach is proposed to maximize the value of currency portfolios over time. The main results of the paper include four parts: Firstly, under the assumptions about the currency market, the currency portfolio optimization problem is formulated as the basic model, in which there are two types of variables describing currency amounts in portfolios and the amount of each currency exchanged into another, respectively. Secondly, the rank one approximation problem and its variants are also formulated to approximate a foreign exchange rate matrix, whose performance is measured by the Frobenius norm or the 2norm of a residual matrix. The intrinsic robustness of the rank one approximation is proved together with summarizing properties of the basic ROA problem and designing a modified power method to search for the virtual exchange rates hidden in a foreign exchange rate matrix. Thirdly, a technique for decision variables reduction is presented to attack the currency portfolio optimization. The reduced formulation is referred to as the ROA model, which keeps only variables describing currency amounts in portfolios. The optimal solution to the ROA model also induces a feasible solution to the basic model of the currency portfolio problem by integrating forex operations from the ROA model with practical forex rates. Finally, numerical examples are presented to verify the feasibility and e ciency of the intrinsic robust rank one approximation approach. They also indicate that there exists an objective measure for evaluating and optimizing currency portfolios over time, which is related to the virtual standard currency and independent of any real currency selected specially for measurement.
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