Stochastic securities market model with no short-selling

The connection between martingale theory and the notion of arbitrage has been an area of extensive research ever since the seminal works by Kreps (1981) and Harrison and Pliska (1981). In particular, we look at the Fundamental Theorem of Asset Pricing, which states that a market has no arbitrage if and only if there is an equivalent probability measure under which the price process is a martingale. Jouini and Kallal (1995), as well as Carassus, Pham, and Touzi (2001) have studied this theorem in the presence of trading constraints. Specifically, they show that if investors are not allowed to short sell assets then the market satisfies no feasible arbitrage if and only if there is an equivalent probability measure under which the price process is a supermartingale.;This dissertation provides a new, versatile framework that strengthens and expands this theorem. Not only does it provide a simpler proof of the result, but it also demonstrates conditions under which the supermartingale property can be strengthened into a martingale property. This work also highlights certain applications of this theorem. In particular, it applies the theorem to the study of bid-ask spreads and pricing bubbles. It then extends the result to an infinite time horizon, using state price deflators. It finally concludes with a discussion of how to price assets, using state price deflators and linear programming techniques.;Keywords: Fundamental Theorem of Asset Pricing, martingale, arbitrage, short selling, state price deflator.