The definition of time is still an open question when one deals with high frequency time series. If time is simply the calendar time, prices can be modeled as continuous random processes and values resulting from transactions or fixings are discrete samples of this underlying dynamics. On the...

The present study shows how the information on 'hidden' market variables effects optimal investment strategies. We take the point of view of two investors, one who has access to the hidden variables and one who only knows the quotes of a given asset. Following Kelly's theory on investment...

We discuss price variations distributions in foreign exchange markets, characterizing them both in calendar and business time frameworks. The price dynamics is found to be the result of two distinct processes, a multi-variance diffusion and an error process. The presence of the latter, which...

The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What it is well known is that absolute returns have memory on a long time...

A quantitative check of weak efficiency in US dollar/German mark exchange rates is developed using high frequency data. We show the existence of long term return anomalies. We introduce a technique to measure the available information and show it can be profitable following a particular trading rule

We introduce a criterion how to price derivatives in incomplete markets, which is based on the theory of optimal strategies in repeated multiplicative games. Arguments are presented why such growth-optimal strategies should be relevant to the problem of pricing derivatives. Under the assumptions...