  In this work we present an equilibrium formulation for price impacts. This is
motivated by the Buhlmann equilibrium in which assets are sold into a system of
market participants, e.g. a fire sale in systemic risk, and can be viewed as a
generalization of the Esscher premium. Existence and uniqueness of clearing
prices for the liquidation of a portfolio are studied. We also investigate
other desired portfolio properties including monotonicity and concavity. Price
per portfolio unit sold is also calculated. In special cases, we study price
impacts generated by market participants who follow the exponential utility and
power utility.

Mathematical Finance