Foreign exchange market modelling and an on-line portfolio selection algorithm

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In this paper, we introduce a matrix-valued time series model for foreign exchange market. We then formulate trading matrices, foreign exchange options and return options (matrices), as well as on-line portfolio strategies. Moreover, we attempt to predict returns of portfolios by developing a cross rate method. This leads us to construct an on-line portfolio selection algorithm for this model. At the end, we prove the profitability and the universality of our algorithm.