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Summary: Optimal Execution with
Nonlinear Impact Functions
and Trading-Enhanced Risk
Robert F. Almgren
October 2001
Abstract
We determine optimal trading strategies for liquidation of a large
single-asset portfolio to minimize a combination of volatility risk and
market impact costs. We take the market impact cost per share to be
a power law function of the trading rate, with an arbitrary positive
exponent. This includes, for example, the square-root law that has
been proposed based on market microstructure theory. In analogy to
the linear model, we define a "characteristic time" for optimal trading,
which now depends on the initial portfolio size and decreases as exe-
cution proceeds. We also consider a model in which uncertainty of the
realized price is increased by demanding rapid execution; we show that
optimal trajectories are described by a "critical portfolio size" above
which this effect is dominant and below which it may be neglected.
Key words: market impact, trading strategy, liquidity modeling.
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