, Volume 59, Issue 1-2, pp 125-159

Internal Regret in On-Line Portfolio Selection


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.


Philip M. Long
An extended abstract appeared in the Proceedings of the 16th Annual Conference on Learning Theory and 7th Kernel Workshop, Springer, 2003. This article is invited by Machine Learning.
The work of Gilles Stoltz was supported by PAI Picasso grant 02543RM and by the French CNRS research network AS66 (SVM and kernel algorithms), and the work of Gábor Lugosi was supported by DGI grant BMF2000-08.