On stochastic and worst-case models for investing

Elad E. Hazan, Satyen Kale

Research output: Chapter in Book/Report/Conference proceedingConference contribution

21 Scopus citations


In practice, most investing is done assuming a probabilistic model of stock price returns known as the Geometric Brownian Motion (GBM). While often an acceptable approximation, the GBM model is not always valid empirically. This motivates a worst-case approach to investing, called universal portfolio management, where the objective is to maximize wealth relative to the wealth earned by the best fixed portfolio in hindsight. In this paper we tie the two approaches, and design an investment strategy which is universal in the worst-case, and yet capable of exploiting the mostly valid GBM model. Our method is based on new and improved regret bounds for online convex optimization with exp-concave loss functions.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference
Number of pages9
StatePublished - Dec 1 2009
Externally publishedYes
Event23rd Annual Conference on Neural Information Processing Systems, NIPS 2009 - Vancouver, BC, Canada
Duration: Dec 7 2009Dec 10 2009


Other23rd Annual Conference on Neural Information Processing Systems, NIPS 2009
CityVancouver, BC

All Science Journal Classification (ASJC) codes

  • Information Systems


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