We propose a systematic framework for designing adaptive trading strategies that minimize both the mean and the variance of the execution costs. This is achieved by diversifying risk over sequential decisions in discrete time. By incorporating previous trading performance as a state variable, the framework can dynamically adjust the risk-aversion level for future trading. This incorporation also allows the framework to solve the mean-variance problems for different risk aversion factors all at once. After developing this framework, it is then applied to solve three algorithmic trading problems. The first two are trade scheduling problems, which address how to split a large order into sequential small orders in order to best approximate a target price – in our case, either the arrival price, or the Volume-Weighed-Average-Price (VWAP). The third problem is one of optimal execution of the resulting small orders by submitting market and limit orders. Unlike the tradition in both academia and industry of treating the scheduling and order placement problems separately, our approach treats them together and solves them simultaneously.In out-of-sample tests, this unified strategy consistently outperforms strategies that treat the two problems separately.
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Risk diversification framework in algorithmic trading
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