  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.
