A model for price impact

A typical financial model presumes that the prices of traded securities are not affected by an investor's buy and sell orders. From a practical viewpoint this assumption is justified as long as his trading volume remains small enough to be easily covered by market liquidity. An opposite situation occurs, for instance, when an economic agent has to sell a large block of shares over a short period of time; this is an "optimal liquidation" problem.
I present results of our joint work with Peter Bank. We develop a continuous-time model for a large investor trading at market indifference prices. In analogy to the construction of stochastic integrals, we investigate the transition from simple to general predictable strategies. A key role is played by a stochastic differential equation for the market makers' utility process. The analysis of this equation relies on conjugacy relationships between the stochastic processes with values in the spaces of saddle functions associated with the representative agent's utility. Two preprints on the subject are available on http://www.math.cmu.edu/~kramkov/publications.html