Internal regret in on-line portfolio selection

G. STOLTZ, G. Lugosi

Machine Learning

May 2005, vol. 59, n°1, pp.125-159

Departments: Economics & Decision Sciences

Keywords: Individual sequences, Internal regret, On-line investment, Universal Portfolio, EG strategy

This paper extends the game-theoretic notion of internal regret to the case of on-line potfolio selection problems. New sequential investment strategies are designed to minimize the cumulative internal regret for all possible market behaviors. Some of the introduced strategies, apart from achieving a small internal regret, achieve an accumulated wealth almost as large as that of the best constantly rebalanced portfolio. It is argued that the low-internal-regret property is related to stability and experiments on real stock exchange data demonstrate that the new strategies achieve better returns compared to some known algorithms.