This chapter introduces the notion of a self-financing, replicating portfolio, a key component of option valuation models. Such a portfolio is based on underlying assets whose values are assumed to be discrete-time random processes. A discrete-time filtration on a probability space is a finite or infinite sequence of σ-fields. A filtration may be viewed as a mathematical description of the information gradually revealed by an experiment evolving in time, for example, one consisting of repeated trials. The filtration consisted of σ-fields generated by partitions. It turns out that any filtration on a finite sample space is of this form. The filtration models the accumulation of stock price information in the discrete time interval. The chapter presents several alternate ways of characterizing a self-financing portfolio.