Fast universalisation of investment strategies

A universalization of a parameterized investment strategy is an online algorithm whose average daily performance approaches that of the strategy operating with the optimal parameters determined offline in hindsight. We present a general framework for universalizing investment strategies and discuss conditions under which investment strategies are universalizable. We present examples of common investment strategies that fit into our framework. The examples include both trading strategies that decide positions in individual stocks, and portfolio strategies that allocate wealth among multiple stocks. This work extends in a natural way Cover's universal portfolio work. We also discuss the runtime efficiency of universalization algorithms. While a straightforward implementation of our algorithms runs in time exponential in the number of parameters, we show that the efficient universal portfolio computation technique of Kalai and Vempala [Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, Redondo Beach, CA, 2000, pp. 486-491] involving the sampling of log-concave functions can be generalized to other classes of investment strategies, thus yielding provably good approximation algorithms in our framework.