IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1610.05018.html
   My bibliography  Save this paper

An explicit formula for optimal portfolios in complete Wiener driven markets: a functional It\^o calculus approach

Author

Listed:
  • Kristoffer Lindensjo

Abstract

We consider a standard optimal investment problem in a complete financial market driven by a Wiener process and derive an explicit formula for the optimal portfolio process in terms of the vertical derivative from functional It^o calculus. An advantage with this approach compared to the Malliavin calculus approach is that it relies only on an integrability condition.

Suggested Citation

  • Kristoffer Lindensjo, 2016. "An explicit formula for optimal portfolios in complete Wiener driven markets: a functional It\^o calculus approach," Papers 1610.05018, arXiv.org, revised Dec 2017.
    • Handle: RePEc:arx:papers:1610.05018
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1610.05018
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cvitanic, Jaksa & Goukasian, Levon & Zapatero, Fernando, 2003. "Monte Carlo computation of optimal portfolios in complete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 971-986, April.
    2. Jérôme B. Detemple & Ren Garcia & Marcel Rindisbacher, 2003. "A Monte Carlo Method for Optimal Portfolios," Journal of Finance, American Finance Association, vol. 58(1), pages 401-446, February.
    3. Jér^me Detemple & Marcel Rindisbacher, 2005. "Closed‐Form Solutions For Optimal Portfolio Selection With Stochastic Interest Rate And Investment Constraints," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 539-568, October.
    4. Fred Espen Benth & Giulia Di Nunno & Arne Løkka & Bernt Øksendal & Frank Proske, 2003. "Explicit Representation of the Minimal Variance Portfolio in Markets Driven by Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 55-72, January.
    5. Peter Lakner & Lan Ma Nygren, 2006. "Portfolio Optimization With Downside Constraints," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 283-299, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Thijs Kamma & Antoon Pelsser, 2019. "Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading Constraints," Papers 1906.12317, arXiv.org, revised Oct 2019.
    2. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    3. Chenxu Li & Olivier Scaillet & Yiwen Shen, 2020. "Wealth Effect on Portfolio Allocation in Incomplete Markets," Papers 2004.10096, arXiv.org, revised Aug 2021.
    4. Chenxu Li & O. Scaillet & Yiwen Shen, 2020. "Decomposition of Optimal Dynamic Portfolio Choice with Wealth-Dependent Utilities in Incomplete Markets," Swiss Finance Institute Research Paper Series 20-22, Swiss Finance Institute.
    5. Jérôme Detemple, 2014. "Portfolio Selection: A Review," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 1-21, April.
    6. Abraham Lioui, 2005. "Stochastic dividend yields and derivatives pricing in complete markets," Review of Derivatives Research, Springer, vol. 8(3), pages 151-175, December.
    7. Jérôme Detemple & René Garcia & Marcel Rindisbacher, 2005. "Asymptotic Properties of Monte Carlo Estimators of Derivatives," Management Science, INFORMS, vol. 51(11), pages 1657-1675, November.
    8. Castañeda, Pablo & Reus, Lorenzo, 2019. "Suboptimal investment behavior and welfare costs: A simulation based approach," Finance Research Letters, Elsevier, vol. 30(C), pages 170-180.
    9. Mkaouar, Farid & Prigent, Jean-Luc & Abid, Ilyes, 2017. "Long-term investment with stochastic interest and inflation rates: The need for inflation-indexed bonds," Economic Modelling, Elsevier, vol. 67(C), pages 228-247.
    10. Suleyman Basak & Dmitry Makarov, 2014. "Strategic Asset Allocation in Money Management," Journal of Finance, American Finance Association, vol. 69(1), pages 179-217, February.
    11. Chabakauri, Georgy, 2012. "Asset pricing with heterogeneous investors and portfolio constraints," LSE Research Online Documents on Economics 119046, London School of Economics and Political Science, LSE Library.
    12. Rytchkov, Oleg, 2016. "Time-Varying Margin Requirements and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 51(2), pages 655-683, April.
    13. Legendre, François & Togola, Djibril, 2016. "Explicit solutions to dynamic portfolio choice problems: A continuous-time detour," Economic Modelling, Elsevier, vol. 58(C), pages 627-641.
    14. Farid Mkouar & Jean-Luc Prigent, 2014. "Long-Term Investment with Stochastic Interest and Inflation Rates Incompleteness and Compensating Variation," Working Papers 2014-301, Department of Research, Ipag Business School.
    15. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    16. Simon Ellersgaard, 2019. "On the Numerical Solution of Mertonian Control Problems: A Survey of the Markov Chain Approximation Method for the Working Economist," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1179-1211, October.
    17. Lioui, Abraham & Tarelli, Andrea, 2019. "Macroeconomic environment, money demand and portfolio choice," European Journal of Operational Research, Elsevier, vol. 274(1), pages 357-374.
    18. Yichen Zhu & Marcos Escobar-Anel, 2021. "A Neural Network Monte Carlo Approximation for Expected Utility Theory," JRFM, MDPI, vol. 14(7), pages 1-18, July.
    19. André Palma & Jean-Luc Prigent, 2009. "Standardized versus customized portfolio: a compensating variation approach," Annals of Operations Research, Springer, vol. 165(1), pages 161-185, January.
    20. Björn Bick & Holger Kraft & Claus Munk, 2013. "Solving Constrained Consumption-Investment Problems by Simulation of Artificial Market Strategies," Management Science, INFORMS, vol. 59(2), pages 485-503, June.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1610.05018. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.