IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1307.0785.html
   My bibliography  Save this paper

Explicit Description of HARA Forward Utilities and Their Optimal Portfolios

Author

Listed:
  • Tahir Choulli
  • Junfeng Ma

Abstract

This paper deals with forward performances of HARA type. Precisely, for a market model in which stock price processes are modeled by a locally bounded $d$-dimensional semimartingale, we elaborate a complete and explicit characterization for this type of forward utilities. Furthermore, the optimal portfolios for each of these forward utilities are explicitly described. Our approach is based on the minimal Hellinger martingale densities that are obtained from the important statistical concept of Hellinger process. These martingale densities were introduced recently, and appeared herein tailor-made for these forward utilities. After outlining our parametrization method for the HARA forward, we provide illustrations on discrete-time market models. Finally, we conclude our paper by pointing out a number of related open questions.

Suggested Citation

  • Tahir Choulli & Junfeng Ma, 2013. "Explicit Description of HARA Forward Utilities and Their Optimal Portfolios," Papers 1307.0785, arXiv.org.
    • Handle: RePEc:arx:papers:1307.0785
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1307.0785
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    3. Michail Anthropelos, 2011. "Forward Exponential Performances: Pricing and Optimal Risk Sharing," Papers 1109.3908, arXiv.org, revised Mar 2013.
    4. Henderson, Vicky & Hobson, David, 2007. "Horizon-unbiased utility functions," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1621-1641, November.
    5. (**), 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.
    6. Tahir Choulli & Christophe Stricker & Jia Li, 2007. "Minimal Hellinger martingale measures of order q," Finance and Stochastics, Springer, vol. 11(3), pages 399-427, July.
    7. Choulli, Tahir & Stricker, Christophe, 2009. "Comparing the minimal Hellinger martingale measure of order q to the q-optimal martingale measure," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1368-1385, April.
    8. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    9. Jonathan Evans & Vicky Henderson & David Hobson, 2008. "Optimal Timing For An Indivisible Asset Sale," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 545-567, October.
    10. M. Musiela & T. Zariphopoulou, 2009. "Portfolio choice under dynamic investment performance criteria," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 161-170.
    11. Hakansson, Nils H, 1969. "Optimal Investment and Consumption Strategies under Risk, an Uncertain Lifetime, and Insurance," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(3), pages 443-466, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tahir Choulli & Jun Deng & Junfeng Ma, 2015. "How non-arbitrage, viability and numéraire portfolio are related," Finance and Stochastics, Springer, vol. 19(4), pages 719-741, October.

    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. Tahir Choulli & Sina Yansori, 2022. "Log-optimal and numéraire portfolios for market models stopped at a random time," Finance and Stochastics, Springer, vol. 26(3), pages 535-585, July.
    2. Tahir Choulli & Sina Yansori, 2018. "Explicit description of all deflators for market models under random horizon with applications to NFLVR," Papers 1803.10128, arXiv.org, revised Feb 2021.
    3. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio and num\'eraire portfolio for market models stopped at a random time," Papers 1810.12762, arXiv.org, revised Aug 2020.
    4. Tahir Choulli & Sina Yansori, 2018. "Log-optimal portfolio without NFLVR: existence, complete characterization, and duality," Papers 1807.06449, arXiv.org.
    5. Michail Anthropelos, 2011. "Forward Exponential Performances: Pricing and Optimal Risk Sharing," Papers 1109.3908, arXiv.org, revised Mar 2013.
    6. Julien Hugonnier & Florian Pelgrin, 2013. "Health and (Other) Asset Holdings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 663-710.
    7. Grasselli, Matheus & Henderson, Vicky, 2009. "Risk aversion and block exercise of executive stock options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 109-127, January.
    8. Qian Lin & Xianming Sun & Chao Zhou, 2019. "Horizon-unbiased Investment with Ambiguity," Papers 1904.09379, arXiv.org.
    9. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    10. David M. Kreps & Walter Schachermayer, 2020. "Convergence of optimal expected utility for a sequence of discrete‐time markets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1205-1228, October.
    11. Mousa, A.S. & Pinheiro, D. & Pinto, A.A., 2016. "Optimal life-insurance selection and purchase within a market of several life-insurance providers," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 133-141.
    12. Wing Fung Chong & Gechun Liang, 2018. "Optimal investment and consumption with forward preferences and uncertain parameters," Papers 1807.01186, arXiv.org, revised Nov 2023.
    13. Kwak, Minsuk & Shin, Yong Hyun & Choi, U Jin, 2011. "Optimal investment and consumption decision of a family with life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 176-188, March.
    14. de Kort, J. & Vellekoop, M.H., 2017. "Existence of optimal consumption strategies in markets with longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 107-121.
    15. Goncalo dos Reis & Vadim Platonov, 2020. "Forward utility and market adjustments in relative investment-consumption games of many players," Papers 2012.01235, arXiv.org, revised Mar 2022.
    16. Yang Wang & Jianwei Lin & Dandan Chen & Jizhou Zhang, 2023. "Optimal Investment–Consumption–Insurance Problem of a Family with Stochastic Income under the Exponential O-U Model," Mathematics, MDPI, vol. 11(19), pages 1-19, October.
    17. Gechun Liang & Moris S. Strub & Yuwei Wang, 2023. "Predictable Relative Forward Performance Processes: Multi-Agent and Mean Field Games for Portfolio Management," Papers 2311.04841, arXiv.org, revised Dec 2023.
    18. Mahan Tahvildari, 2021. "Forward indifference valuation and hedging of basis risk under partial information," Papers 2101.00251, arXiv.org.
    19. Ferdoos Alharbi & Tahir Choulli, 2022. "Log-optimal portfolio after a random time: Existence, description and sensitivity analysis," Papers 2204.03798, arXiv.org.
    20. Sigrid Källblad & Jan Obłój & Thaleia Zariphopoulou, 2018. "Dynamically consistent investment under model uncertainty: the robust forward criteria," Finance and Stochastics, Springer, vol. 22(4), pages 879-918, October.

    More about this item

    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:1307.0785. 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.