A liquidity trader wishes to trade a ?xed number of shares within a certain time horizon and to minimize the mean and variance of the costs of trading. Explicit formulas for the optimal trading strategies show that risk-averse liquidity traders reduce their order sizes over time and execute a higher fraction of their total trading volume in early periods when price volatility or liquidity increases. In the presence of transaction fees, numerical simulations suggest that traders want to trade more frequently when price volatility goes up or liquidity declines. In the multi-asset case, price effects across assets have a substantial impact on trading behavior, as does continuous-time trading.
Huberman, Gur, and Werner Stanzl. "Optimal Liquidity Trading." Review of Finance 9, no. 2 (2005): 165-200.
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