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Mean-Variance Optimal Adaptive Execution Julian Lorenz

Summary: Mean-Variance Optimal Adaptive Execution
Julian Lorenz
and Robert Almgren
January 23, 2011
Electronic trading of equities and other securities makes heavy use
of "arrival price" algorithms, that balance the market impact cost of
rapid execution against the volatility risk of slow execution. In the
standard formulation, mean-variance optimal trading strategies are
static: they do not modify the execution speed in response to price
motions observed during trading. We show that substantial improve-
ment is possible by using dynamic trading strategies, and that the
improvement is larger for large initial positions.
We develop a technique for computing optimal dynamic strategies
to any desired degree of precision. The asset price process is observed
on a discrete tree with a arbitrary number of levels. We introduce a
novel dynamic programming technique in which the control variables
are not only the shares traded at each time step, but also the maxi-
mum expected cost for the remainder of the program; the value func-
tion is the variance of the remaining program. The resulting adaptive


Source: Almgren, Robert F. - Courant Institute of Mathematical Sciences, New York University


Collections: Mathematics