Speaker: Sam Ganzfried
Title: An application of online learning to algorithmic trading.
Date: 28th February, 2006.

This talk will be based mostly on the recent paper “Trading in Markovian Price Models” by Kearns/Kakade (COLT ’05). In a Markovian model for the price evolution of a stock, the probability of local upward or downward movement is arbitrarily dependent on the current price itself (and perhaps some auxiliary state information). This model directly and considerably generalizes many of the most well-studied price evolution models in classical finance, including a variety of random walk, drift, and diffusion models. The main result is a “universally profitable” trading strategy – a single fixed strategy whose profitability competes with the optimal strategy (which knows all of the underlying parameters of the infinite and possibly nonstationary Markov process).

I’ll be discussing both theoretical results and practical issues not addressed in the paper. One interesting aspect of this paper – practicality aside – is that it provides a rigorous analysis of a model that falls between the strong statistical assumptions of classical finance models and the highly adversarial models that appear in theoretical computer science. The weighted majority algorithm (Littlestone, Warmuth), or “best expert” weighting scheme (Cesa-Bianchi et al.) will be relevant to our analysis, and I’ll discuss it and its relation to the general online learning problem. I’ll also introduce all relevant terminology from finance and trading, so no prior background will be necessary. I’m hoping to cover a lot of material, so it’s likely that I’ll need a second talk to finish the presentation.