Efficient Universal Portfolios for Past‐Dependent Target Classes

Jason E. Cross and Andrew R. Barron

Mathematical Finance, 2003, vol. 13, issue 2, 245-276

Abstract: We present a new universal portfolio algorithm that achieves almost the same level of wealth as could be achieved by knowing stock prices ahead of time. Specifically the algorithm tracks the best in hindsight wealth achievable within target classes of linearly parameterized portfolio sequences. The target classes considered are more general than the standard constant rebalanced portfolio class and permit portfolio sequences to exhibit a continuous form of dependence on past prices or other side information. A primary advantage of the algorithm is that it is easily computable in a polynomial number of steps by way of simple closed‐form expressions. This provides an edge over other universal algorithms that require both an exponential number of computations and numerical approximation.

Date: 2003
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