Corrections to the prices of derivatives due to market incompleteness and price impact

We consider two separate problems that are related to each other in the sense that we compute corrections to the linear prices of derivatives due to market incompleteness and price impact.;In the first chapter we explicitly compute price corrections to contingent claims due to market incompleteness in three different models: a model with stochastic volatility, a model with basis risk and a market portfolio, and a credit-risk model with jumps and stochastic recovery rate.;In the second chapter we consider an illiquid market consisting of a large investor and a market maker. The large investor is characterized by his or her demand for the illiquid asset. The market maker is characterized by the utility function U defined on the whole real line. The market makers quotes the prices for the illiquid asset in such a way that his or her terminal wealth maximizes the expected utility. The trading activity of the large investor influences the prices quoted by the market maker, which makes hedging not possible in the classical sense. We provide the solution to the hedging problem for the large investor for a wide class of utility functions and contingent claims. We also compute the recursive price process of a contingent claim under a piecewise constant demand for an exponential utility function of the market maker, as well as its asymptotic expansion.