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An intrinsic robust rank-one-approximation 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

Special Issue: Financial Big Data Technology and Its Applications

A currency portfolio is a special kind of wealth whose value fluctuates with foreignexchange rates over time, which possesses 3Vs (volume, variety and velocity) properties of big datain the currency market. In this paper, an intrinsic robust rank one approximation (ROA) approachis proposed to maximize the value of currency portfolios over time. The main results of the paperinclude four parts: Firstly, under the assumptions about the currency market, the currency portfoliooptimization problem is formulated as the basic model, in which there are two types of variablesdescribing 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 toapproximate a foreign exchange rate matrix, whose performance is measured by the Frobenius normor the 2-norm of a residual matrix. The intrinsic robustness of the rank one approximation is provedtogether with summarizing properties of the basic ROA problem and designing a modified powermethod 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 describingcurrency amounts in portfolios. The optimal solution to the ROA model also induces a feasible solutionto the basic model of the currency portfolio problem by integrating forex operations from the ROAmodel with practical forex rates. Finally, numerical examples are presented to verify the feasibility ande ciency of the intrinsic robust rank one approximation approach. They also indicate that there existsan objective measure for evaluating and optimizing currency portfolios over time, which is related tothe virtual standard currency and independent of any real currency selected specially for measurement.
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Keywords currency portfolio optimization; foreign exchange rate; robust rank one approximation; virtual standard currency; modified power method; variables reduction

Citation: Hongxuan Huang, Zhengjun Zhang. An intrinsic robust rank-one-approximation approach for currency portfolio optimization. Quantitative Finance and Economics, 2018, 2(1): 160-189. doi: 10.3934/QFE.2018.1.160

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