Abstract:
A new application of the Foster–Vohra method of calibration to stock market games will be presented. We present a universal method for algorithmic trading in Stock Market which performs asymptotically at least as well as any stationary trading strategy that computes the investment at each step using a xed function of the side information that belongs to a given RKHS (Reproducing Kernel Hilbert Space). Using a universal kernel, we extend this result for any continuous stationary strategy. In this learning process, a trader chooses his gambles using predictions made by a randomized well-calibrated algorithm. Our strategy is based on Dawid's notion of calibration with more general checking rules and on some modi cation of Kakade and Foster's randomized
rounding algorithm for computing the well-calibrated forecasts. We combine the method of randomized calibration with Vovk's method of defensive forecasting in RKHS. Unlike in statistical theory, no stochastic assumptions are made about the stock prices. Our empirical results on historical markets provide strong evidence that this type of technical trading can "beat" some generally accepted trading strategies if transaction costs are ignored.
