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When to Sell an Asset? - A Distribution Builder Approach

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  • Peter Carr
  • Stephan Sturm

Abstract

We consider the question of the optimal timing of the sale of an asset with stochastic dynamics. Our analysis is based on the method of the distribution builder introduced by Sharpe, Goldstein and Blythe [SGB00] for the purpose of optimal portfolio selection. Instead of specifying a utility function or risk aversion coefficient, this tool directly elicits the target distribution of the investor. We show how the problem of an optimal asset sale is in this setting linked to the problem of finding a Skorokhod embedding of a distribution into a diffusion process. In the case where the asset process follows a geometric Brownian motion and a specific family of distributions is targeted, one can observe a risk-return tradeoff.

Suggested Citation

  • Peter Carr & Stephan Sturm, 2026. "When to Sell an Asset? - A Distribution Builder Approach," Papers 2608.18783, arXiv.org.
    • Handle: RePEc:arx:papers:2608.18783
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    References listed on IDEAS

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    5. Cox, A. M. G. & Hobson, D. G., 2004. "An optimal Skorokhod embedding for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 17-39, May.
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