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Optimal investment with derivative securities

Author

Listed:
  • Aytaç Ílhan
  • Mattias Jonsson
  • Ronnie Sircar

Abstract

We consider an investor who maximizes expected exponential utility of terminal wealth, combining a static position in derivative securities with a traditional dynamic trading strategy in stocks. Our main result, obtained by studying the strict concavity of the utility-indifference price as a function of the static positions, is that, in a quite general incomplete arbitrage-free market, there exists a unique optimal strategy for the investor. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Aytaç Ílhan & Mattias Jonsson & Ronnie Sircar, 2005. "Optimal investment with derivative securities," Finance and Stochastics, Springer, vol. 9(4), pages 585-595, October.
    • Handle: RePEc:spr:finsto:v:9:y:2005:i:4:p:585-595
    DOI: 10.1007/s00780-005-0154-y
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    Citations

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    Cited by:

    1. Jinbeom Kim & Tim Leung, 2016. "Impact of risk aversion and belief heterogeneity on trading of defaultable claims," Annals of Operations Research, Springer, vol. 243(1), pages 117-146, August.
    2. Pietro Siorpaes, 2015. "Optimal investment and price dependence in a semi-static market," Finance and Stochastics, Springer, vol. 19(1), pages 161-187, January.
    3. Weidong Tian & Daisuke Yoshikawa, 2017. "Analyzing Equilibrium in Incomplete Markets with Model Uncertainty," International Review of Finance, International Review of Finance Ltd., vol. 17(2), pages 235-262, June.
    4. Walter Mudzimbabwe, 2020. "A time consistent derivative strategy," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-25, March.
    5. Johannes Gerer & Gregor Dorfleitner, 2016. "A Note On Utility Indifference Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-17, September.
    6. Scott Robertson & Konstantinos Spiliopoulos, 2014. "Indifference pricing for Contingent Claims: Large Deviations Effects," Papers 1410.0384, arXiv.org, revised Feb 2016.
    7. 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.
    8. Tim Leung & Yoshihiro Shirai, 2015. "Optimal derivative liquidation timing under path-dependent risk penalties," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 1-32.
    9. Zeng, Yan & Li, Danping & Chen, Zheng & Yang, Zhou, 2018. "Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 88(C), pages 70-103.
    10. L.J. Basson & Sune Ferreira-Schenk & Zandri Dickason-Koekemoer, 2022. "Fractal Dimension Option Hedging Strategy Implementation During Turbulent Market Conditions in Developing and Developed Countries," International Journal of Economics and Financial Issues, Econjournals, vol. 12(2), pages 84-95, March.
    11. Chen, Jingnan, 2020. "Optimal liquidation of financial derivatives," Finance Research Letters, Elsevier, vol. 34(C).
    12. Chen, Zheng & Li, Zhongfei & Zeng, Yan, 2023. "Portfolio choice with illiquid asset for a loss-averse pension fund investor," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 60-83.
    13. Michail Anthropelos & Gordan Zitkovic, 2008. "On Agents' Agreement and Partial-Equilibrium Pricing in Incomplete Markets," Papers 0803.2198, arXiv.org.
    14. Ilhan, Aytaç & Jonsson, Mattias & Sircar, Ronnie, 2009. "Optimal static-dynamic hedges for exotic options under convex risk measures," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3608-3632, October.
    15. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2018. "Optimal Investment, Demand and Arbitrage under Price Impact," Papers 1804.09151, arXiv.org, revised Dec 2018.
    16. 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.
    17. Sara Biagini & Mustafa Pinar, 2012. "The best gain-loss ratio is a poor performance measure," Papers 1209.6439, arXiv.org, revised Dec 2012.
    18. Li, Danping & Shen, Yang & Zeng, Yan, 2018. "Dynamic derivative-based investment strategy for mean–variance asset–liability management with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 72-86.
    19. Yuan-Hung Hsuku, 2007. "Dynamic consumption and asset allocation with derivative securities," Quantitative Finance, Taylor & Francis Journals, vol. 7(2), pages 137-149.

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