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Optimal investment and price dependence in a semi-static market


  • Pietro Siorpaes



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

    1. Aytaç İlhan & Ronnie Sircar, 2006. "Optimal Static-Dynamic Hedges For Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 359-385.
    2. Friedrich Hubalek & Walter Schachermayer, 1998. "When Does Convergence of Asset Price Processes Imply Convergence of Option Prices?," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 385-403.
    3. Larsen, Kasper & Zitkovic, Gordan, 2007. "Stability of utility-maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1642-1662, November.
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    5. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474,
    6. Elyès Jouini & Clotilde Napp, 2004. "Convergence of utility functions and convergence of optimal strategies," Finance and Stochastics, Springer, vol. 8(1), pages 133-144, January.
    7. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293,
    8. Nicole El Karoui & Monique Jeanblanc-Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126.
    9. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373.
    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.
    11. Kardaras, Constantinos, 2010. "The continuous behavior of the numéraire portfolio under small changes in information structure, probabilistic views and investment constraints," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 331-347, March.
    12. Kasper Larsen, 2009. "Continuity Of Utility-Maximization With Respect To Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 237-250.
    13. Martin Schweizer & Johannes Wissel, 2008. "Term Structures Of Implied Volatilities: Absence Of Arbitrage And Existence Results," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 77-114.
    14. Jean Jacod & Philip Protter, 2010. "Risk-neutral compatibility with option prices," Finance and Stochastics, Springer, vol. 14(2), pages 285-315, April.
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    16. Luciano Campi, 2004. "Arbitrage and completeness in financial markets with given N-dimensional distributions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(1), pages 57-80, August.
    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.
    19. Aytaç Ílhan & Mattias Jonsson & Ronnie Sircar, 2005. "Optimal investment with derivative securities," Finance and Stochastics, Springer, vol. 9(4), pages 585-595, October.
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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,, 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,, revised Feb 2016.

    More about this item


    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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