In this book, the authors investigate structural aspects of no arbitrage pricing of contingent claims and applications of the general pricing theory in the context of incomplete markets. A quasi-closed form pricing equation in terms of artificial probabilities is derived for arbitrary payoff structures. Moreover, a comparison between continuous and discrete models is presented, highlighting the major similarities and key differences. As applications, two sources of market incompleteness are considered, namely shastic volatility and shastic liquidity. Firstly, the general theory discussed before is applied to the pricing of power options in a shastic volatility model. Secondly, the issue of liquidity risk is considered by focusing on the aspect of how asset price dynamics are affected by the trading strategy of a large investor.