Abstract:

When executing a large order of stocks in a market, one important factor in
forming the optimal trading strategy is to consider the price impact of large-volume
trading activity. Minimizing a risk measure of the implementation shortfall, i.e., the
difference between the value of a trader’s initial equity position and the sum of cash
flow he receives from his trading process, is essentially a stochastic control problem.
In this study, we investigate such a practical problem under a dynamic coherent risk
measure in a market in which the stock price dynamics has a feature of momentum
effect. We develop a fast approximation solution scheme, which is critical in highfrequency
trading. We demonstrate some prominent features of our derived solution
algorithm in providing useful guidance for real implementation.

Key words: Nested coherent risk measure ·, Momentum effect ·, Approximation
solution scheme ·, Stochastic dynamic programming