This book explores screen-based trading with an open order book, where traders' decisions influence others in real time via that open order book. Modelling traders’ actions using discrete choice, a method proven in other fields but new to finance, and the integration of discrete choice into a Markov Process, offers an innovative approach to understanding decision making under uncertainty. We call this combination "Doubly Stochastic Markov Process" (DSMP for short). The book is aimed at those interested in real market performance with traders’ modelling based on behavioural expertise. Monitoring orders instead of prices creates a competitive advantage because the adjustment of prices requires prior adjustment of orders. Only the matching of orders generates transactions and prices. Efficient order management turns risky volatility into profits. The presentation of DSMP is preceded by an introductory overview of trading venues and concludes with an outlook on the increasing suitability of stochastic processes to implement the interactions of agents and to facilitate modelling the self-organisation of markets.