Calibration with Changing Checking Rules and Its Application to Short-Term Trading

We provide a natural learning process in which a financial trader without a risk receives a gain in case when Stock Market is inefficient. In this process, the trader rationally choose his gambles using a prediction made by a randomized calibrated algorithm. Our strategy is based on Dawid's notion of calibration with more general changing checking rules and on some modification of Kakade and Foster's randomized algorithm for computing calibrated forecasts.