Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 2002,53
We introduce a general continuous-time model for an illiquid financial market where the trades of a single large investor can move market prices. The model is specified in terms of parameter dependent semimartingales, and its mathematical analysis relies on the non-linear integration theory of such semimartingale families. The Itô-Wentzell formula is used to prove absence of arbitrage for the large investor, and using approximation results for stochastic integrals, we characterize the set of approximately attainable claims. We furthermore show how to compute superreplication prices and discuss the large investor's utility maximization problem.
large investor feedback effect parameter dependent semimartingales uniform approximation of stochastic integrals Itô-Wentzell formula