This dissertation considers the pricing and hedging of contingent claims in a generalsemimartingale market. Initially the focus is on a complete market, where it ispossible to price uniquely and hedge perfectly. In this context the two fundamentaltheorems of asset pricing are explored. The...

Contingent claims with payoffs depending on finitely many asset prices are modeled as elements of a separable Hilbert space. Under fairly general conditions, including market completeness, it is shown that one may change measure to a reference measure under which asset prices are Gaussian and...

The assumption of the complete market simplifies the whole theory of arbitrage pricing theory since the pioneering work of Black and Scholes. The martingale approach is one of the most powerful tool for pricing derivative securities in the complete market. The existence of such a market,...

This paper addresses the applicability of the convex duality method for utility maximization, in the presence of random endowment. When the price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true, for a wide class of utility functions and...