Optimal Liquidation with Support and Resistance in a Multi-Skew Price Model

Summary

The document studies when to liquidate an asset whose price follows a geometric multi-skew Brownian motion. The model represents support and resistance through local-time effects: price receives an upward push at support and a downward push at resistance. It keeps the price process Markovian using price alone, then analyzes the perpetual liquidation problem within that framework.

The solution yields three possible continuation-band geometries, distinguished by a closed-form criterion: the band can remain below resistance, cross it, or end at resistance. The analysis concludes that selling into resistance can emerge from the optimization rather than being imposed in advance. It also finds asymmetric identification: observed exercise behavior pins down support parameters, while resistance strength can only be identified within an interval with a closed-form endpoint. The excerpt gives no empirical validation or detail on assumptions, so its conclusions are specific to the stated model.

Key ideas

• The model represents support and resistance through local-time pushes in a price-only Markov process.
• The perpetual liquidation solution has three continuation-band geometries separated by a closed-form criterion.
• The optimal policy may place the upper edge of the continuation band at resistance.
• Exercise behavior identifies support parameters exactly, while resistance strength is identified only within an interval.

Tags

# Optimal Liquidation with Support and Resistance Levels under Multi-Skew Brownian Motion


# Optimal Liquidation with Support and Resistance Levels under Multi-Skew Brownian Motion









We solve the perpetual liquidation problem for a geometric multi-skew Brownian motion carrying local-time pushes upward at a support level and downward at a resistance level, a model of technical analysis that is Markov in the price alone. Three geometries arise, separated by a closed-form criterion: the continuation band lies below resistance, straddles it, or pins its upper edge there. Selling into resistance is a conclusion rather than an assumption. Identification is asymmetric: exercise behaviour determines the support parameters exactly, while the strength of resistance is recoverable only on an interval with a closed-form endpoint.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.