Several empirical studies have shown the inadequacy of the standard Brownian motion (sBm) as a model of asset returns. To correct for this evidence some authors have conjectured that asset returns may be independently and identically Pareto-Lévy stable (PLs) distributed, whereas others have...

This chapter introduces the reader to definitions and key properties of stochastic processes that are important in finance. The discussion starts from the description of Brownian motion that describes the idea of a continuous random walk and proceeds to Ito processes that incorporate both trend...

The purpose of this paper is to solve a stochastic control problem consisting of optimizing the management of a trading system. Two model free machine learning algorithms based on Reinforcement Learning method are compared: the Q-Learning and the SARSA ones. Both these models optimize their...