2010/07/20 by David German, German, David
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Economic theories and models #Stochastic processes and financial applications #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1007.3316
arxiv created 2010/07/20 · arxiv updated 2010/07/21
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.