This thesis studies no-arbitrage pricing and dynamic conic nance for dividend-paying securities in discrete-time markets with transaction... Show moreThis thesis studies no-arbitrage pricing and dynamic conic nance for dividend-paying securities in discrete-time markets with transaction costs. The rst part investigates no-arbitrage pricing for dividend-paying securities in discrete-time markets with transaction costs. We introduce the value process and the self- nancing condition in our context. Then, we prove a version of First Fundamental Theorem of Asset Pricing. Speci cally, we prove that the no-arbitrage condition under the e cient friction assumption is equivalent to the existence of a risk-neutral measure. We formulate an appropriate notion of a consistent pricing system in our set-up, and we prove that if there are no transaction costs on the dividends paid by the securities, then the no-arbitrage condition under the e cient friction assumption is equivalent to the existence of a consistent pricing system. We nish the chapter by deriving dual representations for the superhedging ask price and subhedging bid price of a derivative contract. The second part studies dynamic conic nance in the set-up introduced in the rst part. We formulate the no-good-deal condition in terms of a family of dynamic coherent risk measures, and then we prove a version of the Fundamental Theorem of No-Good-Deal Pricing. The Fundamental Theorem of No-Good-Deal Pricing provides a necessary and su cient condition for the no-good-deal condition to hold. Next, we study the no-good-deal ask and bid prices of a derivative contract. We particularize our results to the dynamic Gain-Loss Ratio, and compute the no-good-deal prices of European-style Asian options in a market with transaction costs. Ph.D. in Applied Mathematics, July 2012 Show less
