A quasi-multi-period model for optimal position liquidation in the presence of market impact is proposed. Two main features distinguish the approach from alternatives. First, a shrinking horizon framework is implemented to update intraday parameters by incorporating new 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 captures traders' increased risk aversion to losses better than symmetric risk measures. The performance of the proposed strategies is tested using historical, high-frequency New York Stock Exchange (NYSE) data. The proposed strategies outperform their benchmark on days with unfavorable market conditions, 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.