We study a financial model with a non-trivial price impact effect. In this model we consider the interaction of a large investor trading in an illiquid security, and a market maker who is quoting prices for this security. We assume that the market maker quotes the prices such that by taking the other side of the investor's demand, the market maker will arrive at maturity with the maximal expected utility of the terminal wealth. Within this model we provide an explicit recursive pricing formula for an exponential utility function, as well as an asymptotic expansion for the price for a "small" simple demand.

We compute the first-order corrections to marginal utility-based prices with respect to a 'small' number of random endowments in the framework of three incomplete financial models. They are a stochastic volatility model, a basis risk and market portfolio model and a credit-risk model with jumps and stochastic recovery rate.Price corrections, risk tolerance, stochastic volatility, basis risk, credit risk,

We review the utility-based valuation method for pricing derivative securities in incomplete markets. In particular, we review the practical approach to the utility-based pricing by the means of computing the first order expansion of marginal utility-based prices with respect to a small number of random endowments.