By Robert Dochow
Robert Dochow mathematically derives a simplified category constitution of chosen different types of the portfolio choice challenge. He proposes new aggressive on-line algorithms with danger administration, which he evaluates analytically. the writer empirically evaluates on-line algorithms by means of a complete statistical research. Concrete effects are that follow-the-loser algorithms express the main promising functionality whilst the target is the maximization of go back on funding and risk-adjusted functionality. additionally, while the target is the minimization of probability, the 2 new algorithms with chance administration convey very good functionality. A prototype of a software program instrument for automatic assessment of algorithms for portfolio choice is given.
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Extra info for Online Algorithms for the Portfolio Selection Problem
The wealth, taking out from A1 is directly converted into wealth invested in A2 and vice versa. The number of shares to be bought (sold) of A1 are directly converted into a number of shares to be sold (bought) of A2 . 10) ensures that consumption is excluded. , 22 2 Portfolio Selection Problems q1t q2t = Q21t . In the absence of transaction costs, a conversion itself does not change the current wealth. The wealth is only effected if the asset prices are changing between time instant t and t + 1.
Asset Prices and Conversion Rates Let qit be the price of Ai at time instant t. Consider a market with two assets (Ai and Aj ) and both are regarded as a conversion pair with Ai as base asset and Aj as counter asset (the terms are based on currency portfolios as described in [Darvas, 2009]). Assume, wealth invested in the base asset is only convertible into wealth invested in the counter asset, denoted as conversion. 1) Qjit = qjt for time instant t. It gives the number of shares of the counter asset which are received if one share of the base asset is sold.
Summing up, this can be formulated by the following research question: Question 1: How to classify selected types of the PSP and evaluate the performance of an algorithm for the PSP? Li and Hoi  provide an extensive survey of algorithms for the PSP from the MLC perspective. This thesis is limited to the algorithms of this survey from the type: benchmark, follow-the-winner and follow-the-loser. Critical on this survey is that the representation of some algorithms is not appropriate for a simple implementation in a trading system.