Universal portfolios and multiplicative updates: A comparison and smoothed guarded update

We present different investment strategies for portfolio selection in a stock market setting. The objective is to maximize the investor's wealth. A well chosen portfolio can do as well or better than the (unknown) best performing stocks. The standard comparison is the wealth that can be achieved by the best constant re-balanced portfolio (BCRP) chosen after the stock outcomes are revealed. We compare other methods that use only past information and examine their performance relative to BCRP. We will also introduce new algorithms and describe conditions under which these new investment strategies exceed the BCRP target wealth.