Trading on a Regime-Change Alarm: Optimal Execution and Portfolio Choice

Markets change regime. A trend fades, order flow turns, and a signal that made money last week starts to lose it. Traders often monitor these breaks with a sequential alarm, which fires once the evidence against the current regime is strong enough. But alarms can be late or simply wrong, so how much should a trader trust one? Our main result is a general theorem that characterises the optimal strategy for a broad class of trading problems in which decisions rely on such an alarm. We apply it to two central problems in finance, namely executing a large order with price impact and allocating a portfolio between risky assets and cash. In both cases, the theorem gives explicit strategies. In execution, the trader does not wait for the alarm, and positions shift ahead of it based on how likely it is to fire before the horizon ends. We also show that the alarm should be calibrated to the trading objective rather than to a purely statistical false-alarm rate, because false alarms and late alarms have different costs in each setting. Finally, simulations compare these strategies with simple rules a trading desk might use, showing where the extra complexity pays off and where it does not.