Abstract
In this chapter we begin our study of multi-period financial markets. We consider a multi-period economy with a finite time horizon in which uncertainty is modelled by a finite sample space. At each date prior to the terminal date, agents can buy or sell a finite number of basic securities at their prevailing price. Each of these securities entitles them to a certain payoff at every successive date. Through their trading activity agents can implement dynamic trading strategies by building portfolios at the starting date and successively rebalancing them until liquidation. Of particular interest are self-financing trading strategies. For these strategies rebalancing is costless, i.e., at each date the set-up of the new portfolio can be financed by the proceeds from the liquidation of the previous portfolio. A payoff that can be generated by way of a self-financing strategy is said to be replicable. The market is said to be complete if all conceivable payoffs can be generated in this way.
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