Chapter 2 Finite state securities market models and arbitrage

Abstract

Publisher Summary A fundamental characteristic of security prices in a competitive securities market is that they do not permit arbitrage opportunities. The number of states in the economy is assumed in the chapter to be finite. This allows for a simple and elegant characterization of arbitrage-free security prices. An analysis of related topics to the theory of arbitrage is presented in the chapter. First, it is analyzed how one can characterize arbitrage-free prices in a frictionless securities market. To this end, the fundamental theorem of asset pricing is proved that links the lack of arbitrage opportunities to the existence of a risk-neutral probability measure. The issue of dynamic completeness is also acknowledged. Second, it is analyzed how to characterize arbitrage-free asset prices in a market where there are costs of trading securities. It is shown how the fundamental theorem of asset pricing needs to be generalized to take account of market frictions. The question of optimal portfolio choice in a complete or incomplete market is also described, with or without transactions costs. The focus is on the optimal portfolio choice behavior of an individual investor who takes as given an arbitrage-free process for asset prices.