2004) : “Hedging and portfolio optimization in illiquid financial markets with a large trader

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 fami-lies. 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 com-pute superreplication prices and discuss the large investor’s utility maximization problem. AMS 2000 subject classification. 60H05, 60H30, 91B28, 91B70 Key words and phrases. large investor, feedback effect, Itô–Wentzell formula, parameter dependent semimartingales, uniform approximation of stochastic integrals Acknowledgement. We would like to thank Hans Föllmer, Rüdiger Frey, and Martin Schweizer for helpful discussions and comments