Multi-Period Models: Portfolio Choice, Equilibrium and No-Arbitrage

In this chapter, we extend the analysis developed in the previous chapters to the case of dynamic multi-period economies. The chapter starts by studying the optimal investment-consumption problem of an individual agent in a multi-period setting, by relying on the dynamic programming approach. Under suitable assumptions on the utility function, closed-form solutions are derived. The chapter then proceeds by extending the general equilibrium theory established in Chap. 4 to a dynamic setting, introducing the notion of dynamic market completeness and analysing the aggregation property of the economy. The fundamental theorem of asset pricing is then established in a multi-period setting and its relation to the equilibrium of the economy is also discussed. Later in the chapter, the most important asset pricing relations presented in Chap. 5 are extended to a dynamic context and specialized for several classes of utility functions. The chapter ends by considering multi-period economies with an infinite time horizon and the possibility of asset price bubbles.