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Utility maximization on the real line under proportional transaction costs

Author

Listed:
  • Bruno Bouchard

    () (Laboratoire de Probabilités et Modèles Aléatoires, University Pierre et Marie Curie, and LFA, CREST, 15 bd Gabriel Péri, 92245 Malakoff Cedex, France Manuscript)

Abstract

We consider a financial market with costs as in Kabanov and Last (1999). Given a utility function defined on ${\mathbb R}$, we analyze the problem of maximizing the expected utility of the liquidation value of terminal wealth diminished by some random claim. We prove that, under the Reasonable asymptotic elasticity conditions introduced by Schachermayer (2000a), existence and duality hold in the class of targets that can be approximated by bounded from below strategies. Under some additional condition, we prove that the optimal target is indeed attainable. As an application, we obtain a dual formulation for the exponential reservation price.

Suggested Citation

  • Bruno Bouchard, 2002. "Utility maximization on the real line under proportional transaction costs," Finance and Stochastics, Springer, vol. 6(4), pages 495-516.
  • Handle: RePEc:spr:finsto:v:6:y:2002:i:4:p:495-516
    Note: received: April 2001; final version received: November 2001
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    Citations

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    Cited by:

    1. Christoph Czichowsky & Walter Schachermayer, 2015. "Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion," Papers 1505.02416, arXiv.org, revised Aug 2016.
    2. Lingqi Gu & Yiqing Lin & Junjian Yang, 2016. "A note on utility maximization with transaction costs and random endoment: num\'eraire-based model and convex duality," Papers 1602.01070, arXiv.org, revised Feb 2016.
    3. Westray, Nicholas & Zheng, Harry, 2009. "Constrained nonsmooth utility maximization without quadratic inf convolution," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1561-1579, May.
    4. repec:spr:finsto:v:22:y:2018:i:1:d:10.1007_s00780-017-0351-5 is not listed on IDEAS
    5. Yiqing Lin & Junjian Yang, 2016. "Utility maximization problem with random endowment and transaction costs: when wealth may become negative," Papers 1604.08224, arXiv.org, revised Sep 2016.
    6. Christoph Czichowsky & R'emi Peyre & Walter Schachermayer & Junjian Yang, 2016. "Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs," Papers 1608.01415, arXiv.org.
    7. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the existence of shadow prices," Working Papers hal-00645980, HAL.
    8. Bruno Bouchard & Ludovic Moreau & Mete H. Soner, 2013. "Hedging under an expected loss constraint with small transaction costs," Papers 1309.4916, arXiv.org, revised Sep 2014.
    9. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, HAL.
    10. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2011. "On the Existence of Shadow Prices," Papers 1111.6633, arXiv.org, revised Jan 2013.
    11. Nicholas Westray & Harry Zheng, 2011. "Minimal sufficient conditions for a primal optimizer in nonsmooth utility maximization," Finance and Stochastics, Springer, vol. 15(3), pages 501-512, September.
    12. Huy N. Chau & Mikl'os R'asonyi, 2016. "Skorohod's representation theorem and optimal strategies for markets with frictions," Papers 1606.07311, arXiv.org, revised Apr 2017.
    13. repec:hal:wpaper:halshs-00664074 is not listed on IDEAS
    14. Giuseppe Benedetti & Luciano Campi & Jan Kallsen & Johannes Muhle-Karbe, 2013. "On the existence of shadow prices," Finance and Stochastics, Springer, vol. 17(4), pages 801-818, October.
    15. Buss, Adrian & Dumas, Bernard J, 2015. "Trading Fees and Slow-Moving Capital," CEPR Discussion Papers 10737, C.E.P.R. Discussion Papers.
    16. Bruno Bouchard & Ludovic Moreau & Mete Soner, 2016. "Hedging under an expected loss constraint with small transaction costs," Post-Print hal-00863562, HAL.
    17. Lingqi Gu & Yiqing Lin & Junjian Yang, 2017. "Utility maximization problem under transaction costs: optimal dual processes and stability," Papers 1710.04363, arXiv.org.
    18. Bouchard, B. & Mazliak, L., 2003. "A multidimensional bipolar theorem in," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 213-231, October.
    19. Luciano Campi & Mark Owen, 2011. "Multivariate utility maximization with proportional transaction costs," Finance and Stochastics, Springer, vol. 15(3), pages 461-499, September.
    20. repec:dau:papers:123456789/2318 is not listed on IDEAS
    21. Miklos Rasonyi, 2017. "On utility maximization without passing by the dual problem," Papers 1702.00982, arXiv.org, revised Mar 2018.
    22. Luciano Campi & Elyès Jouini & Vincent Porte, 2013. "Efficient portfolios in financial markets with proportional transaction costs," Post-Print halshs-00664074, HAL.

    More about this item

    Keywords

    Transaction costs; utility maximization; reasonable asymptotic elasticity; hedging; option pricing;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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