The martingales: theoretical and empirical characteristics

This paper offers an overview on the characteristics of martingales. These latter are markovian processes without underlying trend, in which the stochastic variable depends on its ultimate realisation. Some application fields are in studies relative to financial markets, and especially the derivative securities. Drawing from the theoretical and empirical literature, the main mathematical characteristics are presented. In order to transform processes with increasing or decreasing trends into martingales, the Doob-Meyer decomposition and the change of probability measure approaches can be adopted. Finally, four applications are considered with regard to the pricing of futures, call options and stocks.