On-line portfolio selection using stochastic programming

Abstract

This paper is dedicated to the problem of dynamic portfolio optimization for the case when the number of decision periods is large and new information about market arrives during each such period. We propose the family of adaptive portfolio selection policies which rebalance the current portfolio during each decision period by adopting portfolio from a specified family with the best performance on the past data. In the absence of transaction costs the general conditions are found under which this policy yields asymptotically the same performance as the best portfolio from the same family constructed with the full knowledge of the future. These results are extended for the case of nonzero transaction costs by introducing a class of threshold portfolio optimization policies which rebalance current portfolio only when its performance differs from performance of the best portfolio by a given threshold. The value of this threshold is adapted to the changing market conditions. We show that it is possible to select a sequence of threshold values in such a way that the asymptotic influence of transaction costs on portfolio performance is negligible and overall portfolio performance is asymptotically the same as the performance of portfolio with the perfect knowledge of the future. We do not assume neither specific probabilistic structure of the market data nor their stationarity. Our theory is illustrated by numerical experiments with real data. Finally, we discuss the relevance of our results in the context of high performance computing.