This doctoral dissertation examines different notions of financial randomness and regularity. We show that main financial theories (i.e. market efficiency, behavioral finance and the so-called ''conventionalist approach'') support the impossibility of outperforming the ''buy and hold'' strategy. This point is confirmed by statistical works since regularities identified in financial time series do not help to predict the direction of future returns. To the best of our knowledge, available econometric models often provide too low ''hit scores'' (< 60%) to become successful trading rules. A conceptuel contribution of this work lies in the introduction of algorithmic complexity to finance. A general approach is proposed to estimate the ''Kolmogorov complexity'' of financial returns: lossless compression tools are used to detect regular patterns which could be overlooked by statistical tests. By studying tick-by-tick data from major stock markets, we find a higher complexity for the Euronext-Paris data than for the NYSE and the NASDAQ ones. This result can be explained by their intraday volatility autocorrelations. Supported both by financial theories and by empirical observations, impossibility to outperform the ''buy and hold'' strategy is linked to the common expression ''to outperform the market'' by a new definition for ''unbeatable strings''. With computable functions modeling effective trading rules, a price sequence is said to be ''unbeatable'' if no effective trading rule can generate indefinitely more profits than the ''buy and hold'' alternative.
