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Optimal investment and price dependence in a semi-static market

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  • Pietro Siorpaes

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 modeled as locally-bounded semi-martingales. Using a general utility function defined on the positive real 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.

Suggested Citation

  • Pietro Siorpaes, 2013. "Optimal investment and price dependence in a semi-static market," Papers 1303.0237, arXiv.org, revised Oct 2013.
    • Handle: RePEc:arx:papers:1303.0237
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    References listed on IDEAS

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    1. Kasper Larsen & Gordan Zitkovic, 2007. "Stability of utility-maximization in incomplete markets," Papers 0706.0474, arXiv.org.
    2. 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.
    3. Pietro Siorpaes, 2012. "Optimal Investment with Stocks and Derivatives," Papers 1210.5466, arXiv.org, revised Oct 2013.
    4. Kasper Larsen, 2009. "Continuity Of Utility‐Maximization With Respect To Preferences," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 237-250, April.
    5. 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, January.
    6. Martin Schweizer & Johannes Wissel, 2008. "Arbitrage-free market models for option prices: the multi-strike case," Finance and Stochastics, Springer, vol. 12(4), pages 469-505, October.
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    Cited by:

    1. Erhan Bayraktar & Gu Wang, 2018. "Quantile Hedging in a semi-static market with model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(2), pages 197-227, April.

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