A Primer in Stochastic Integration

In the previous chapters we mainly developed the arbitrage theory for models in finite discrete time. In the setting of the previous chapter, where the probability space was not finite, several features of infinite dimensional functional analysis played a role. When trading takes place in continuous time the difficulties increase even more. It is here that we need the full power of stochastic integration theory. Before giving precise definitions, let us give a short overview of the different models and of their mutual relation.