Multi-Period Models:The Main Issues

Abstract

In this chapter we turn to general multi-period models. We will proceed similarly to Chapter 6. We start by introducing the mathematical model. We then proceed to establish the equivalence of the existence of a linear pricing functional and the validity of the Law of One Price. The next step is the equivalence of the existence of strongly positive linear pricing functionals and the absence of arbitrage opportunities. We finalize the chapter by treating completeness and incomplete markets. The formulation of the multi-period versions of the two Fundamental Theorems of Asset Pricing are left for Chapter 11, since for their formulation, we first need to develop the notion of martingales in Chapter 10.