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Optimal investment and price dependence in a semi-static market

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  • Pietro Siorpaes

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Abstract

This paper studies the problem of maximizing expected utility from terminal wealth in a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously in time and are modelled as locally bounded semimartingales. Using a general utility function defined on the positive half-line, we first study existence and uniqueness of the solution, and then we consider the dependence of the outputs of the utility maximization problem on the price of the derivatives, investigating not only stability but also differentiability, monotonicity, convexity and limiting properties. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Pietro Siorpaes, 2015. "Optimal investment and price dependence in a semi-static market," Finance and Stochastics, Springer, vol. 19(1), pages 161-187, January.
  • Handle: RePEc:spr:finsto:v:19:y:2015:i:1:p:161-187
    DOI: 10.1007/s00780-014-0245-8
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    References listed on IDEAS

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    1. Aytaç İlhan & Ronnie Sircar, 2006. "Optimal Static-Dynamic Hedges For Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 359-385.
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    7. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293, arXiv.org.
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    10. Julien Hugonnier & Dmitry Kramkov & Walter Schachermayer, 2005. "On Utility-Based Pricing Of Contingent Claims In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 203-212.
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    17. repec:dau:papers:123456789/355 is not listed on IDEAS
    18. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
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    Citations

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    Cited by:

    1. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2015. "The pricing of contingent claims and optimal positions in asymptotically complete markets," Papers 1509.06210, arXiv.org, revised Sep 2016.
    2. Erhan Bayraktar & Zhou Zhou, 2015. "Arbitrage, hedging and utility maximization using semi-static trading strategies with American options," Papers 1502.06681, arXiv.org, revised Feb 2016.

    More about this item

    Keywords

    Optimal investment; Convex duality; Incomplete markets; Price dependence; Well-posed problem; 91B16; 49N15; 91G10; G11;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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