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On the minimizers of energy forms with completely monotone kernel

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  • Alexander Schied
  • Elias Strehle

Abstract

Motivated by the problem of optimal portfolio liquidation under transient price impact, we study the minimization of energy functionals with completely monotone displacement kernel under an integral constraint. The corresponding minimizers can be characterized by Fredholm integral equations of the second type with constant free term. Our main result states that minimizers are analytic and have a power series development in terms of even powers of the distance to the midpoint of the domain of definition and with nonnegative coefficients. We show moreover that our minimization problem is equivalent to the minimization of the energy functional under a nonnegativity constraint.

Suggested Citation

  • Alexander Schied & Elias Strehle, 2017. "On the minimizers of energy forms with completely monotone kernel," Papers 1706.04844, arXiv.org, revised Aug 2018.
  • Handle: RePEc:arx:papers:1706.04844
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    File URL: http://arxiv.org/pdf/1706.04844
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    References listed on IDEAS

    as
    1. Aur'elien Alfonsi & Alexander Schied, 2012. "Capacitary measures for completely monotone kernels via singular control," Papers 1201.2756, arXiv.org, revised Feb 2013.
    2. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    3. Aurélien Alfonsi & Alexander Schied, 2013. "Capacitary measures for completely monotone kernels via singular control," Post-Print hal-00659421, HAL.
    4. Alfonsi Aurélien & Alexander Schied & Alla Slynko, 2012. "Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem," Post-Print hal-00941333, HAL.
    5. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
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