Abstract
The purpose of this paper is to study on-line portfolio selection strategies for currency exchange markets and our focus is on the markets with presence of decrements. To this end, we first analyze the main factors arising in the decrements. Then we develop a cross rate scheme which enables us to establish an on-line portfolio selection strategy for the currency exchange markets with presence of decrements. Finally, we prove the universality of our on-line portfolio selections.
Highlights
We are concerned with a currency exchange market in the presence of decrements
The investors can rearrange their portfolio in the profitable direction by using the two update rules FFGD (30) or the Exponential Growth the of Fund with Decrements (EGRFD) (31) with effective Cross Rate (CR)(MPCR, MPO, gk′+1 )
We have shown that the investors follow two update rules with the cross rate method to obtain more than half probability to reschedule the portfolio vector profitability and these update rules can be considered as universality for the investors to measure on-line portfolios, by following the main ideas of [2], but the difference is that our two update ruels with the decrements replace the transaction cost discussed in [2]
Summary
We are concerned with a currency exchange market in the presence of decrements. Our objective is to develop an on-line portfolio selection strategy for such a market. To this end, we utilise a cross rate method to establish a suitable algorithm scheme. The problem of establishing on-line portfolio selection schemes for various financial markets has been well studied (see, e.g. the monograph [1] and a recent paper by Albeverio, Lao, and Zhao [2], and references therein). The on-line portfolio selections can be identified as active portfolio strategies (see, e.g., [2]). An active portfolio means that the currencies to be traded have high
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