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A Shrinking Horizon Optimal Liquidation Framework with Lower Partial Moments Criteria

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Abstract: A novel quasi-multi-period model for optimal position liquidation in the presence of both temporary and permanent market impact is proposed. Two main features distinguish the proposed approach from alternatives. First, a shrinking horizon framework is implemented to update intraday parameters by incorporating new incoming information while maintaining standard non-anticipativity constraints. The method is data-driven, numerically tractable, and reactive to the market. Second, lower partial moments, a downside risk measure, is used which, unlike symmetric measures such as variance, captures traders’ increased risk aversion to losses. The performance of the proposed strategies is tested using historical, high-frequency New York Stock Exchange (NYSE) data. All proposed strategies outperform classic strategies such as a Time Weighted Average Price (TWAP) strategy as well as more unrealistic strategies such as an Ex-post Volume Weighted Average Price (VWAP) strategy that violates non-anticipativity on days with unfavorable market conditions, thus, strongly supporting the use of lower partial moments as a risk measure. Additionally, results validate the use of a shrinking horizon framework as an adaptive, tractable alternative to dynamic programming for trading.

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