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Using Longstaff-Schwartz for Finite-Horizon Asset Sale Timing

Article Quant Q&A · Author: Qwerty
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Summary

The document asks whether Longstaff-Schwartz can determine when to sell a stock within a fixed time horizon, rather than being used only to value derivatives. The answer places the method within the broader class of finite-horizon optimal stopping problems, including Markovian settings.

Dynamic programming for such a problem requires conditional expectations at successive decision points. Longstaff-Schwartz and the Tsitsiklis-Van Roy approach are named as methods for approximating those expectations, so the framework can apply beyond derivative exercise when the asset-sale decision is formulated as an optimal stopping problem. The response is conceptual and brief: it does not specify a stock model, regression basis, stopping rule, transaction costs, or implementation details, nor does it compare estimation accuracy across methods.

Key ideas

  • Finite-horizon asset sale timing can be formulated as an optimal stopping problem.
  • Dynamic programming for optimal stopping requires conditional expectations at decision points.
  • Longstaff-Schwartz can approximate those expectations, as can the Tsitsiklis-Van Roy approach.
  • The answer gives no implementation details or treatment of trading costs.

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EquitiesStatisticsMachine learning
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# Longstaff-Schwartz for any optimal stopping


# Longstaff-Schwartz for any optimal stopping












Let's say I have the stock of General Motors and I assume some fancy model for the price of this stock and I have to sell it within a month. Can I use Longstaff-Schwartz algorithm to determine the best time to sell the stock? I'm asking because I noticed that the algorithm seems to be used only for derivatives, but isn't it more natural to use it to determine when is the best time to sell any asset?

## Answer by d_797 (score 0, accepted)

https://quant.stackexchange.com/a/59198

To solve a standard optimal stopping problem (say Markovian, finite horizon), you must calculate certain conditional expectations that arise in the dynamic programming principle algorithm. These conditional expectations can be approximated using Longstaff-Schwartz or the Tsitsiklis-Van Roy approach, among others.

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