IDEAS home Printed from https://ideas.repec.org/p/arx/papers/math-0207260.html
   My bibliography  Save this paper

Optimal portfolio selection and compression in an incomplete market

Author

Listed:
  • Nikolai Dokuchaev
  • Ulrich Haussmann

Abstract

We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modeled as diffusions and the market is incomplete. We find an explicit solution for the case of limited diversification of the portfolio, i.e. for the portfolio compression problem. By this we mean that an admissible strategies may include no more than m different stocks concurrently, where m may be less than the total number n of available stocks.

Suggested Citation

  • Nikolai Dokuchaev & Ulrich Haussmann, 2002. "Optimal portfolio selection and compression in an incomplete market," Papers math/0207260, arXiv.org.
    • Handle: RePEc:arx:papers:math/0207260
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/math/0207260
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    3. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    4. Zhongquan Zhou, 1998. "An Equilibrium Analysis of Hedging with Liquidity Constraints, Speculation, and Government Price Subsidy in a Commodity Market," Journal of Finance, American Finance Association, vol. 53(5), pages 1705-1736, October.
    5. Jean-Paul Laurent & Huyen Pham, 1999. "Dynamic programming and mean-variance hedging," Post-Print hal-03675953, HAL.
    6. Martin Kulldorff & Ajay Khanna, 1999. "A generalization of the mutual fund theorem," Finance and Stochastics, Springer, vol. 3(2), pages 167-185.
    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. Dokuchaev, Nikolai, 2007. "Discrete time market with serial correlations and optimal myopic strategies," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1090-1104, March.
    2. Nikolai Dokuchaev, 2015. "Optimal portfolio with unobservable market parameters and certainty equivalence principle," Papers 1502.02352, arXiv.org.
    3. Nikolai Dokuchaev, 2002. "Maximin setting for investment problems and fixed income management with observable but non-predictable parameters," Papers math/0207259, arXiv.org.
    4. Nikolai Dokuchaev, 2014. "Mutual Fund Theorem for continuous time markets with random coefficients," Theory and Decision, Springer, vol. 76(2), pages 179-199, February.
    5. Dokuchaev, Nikolai, 2010. "Optimality of myopic strategies for multi-stock discrete time market with management costs," European Journal of Operational Research, Elsevier, vol. 200(2), pages 551-556, January.
    6. Nikolai Dokuchaev, 2015. "Modelling Possibility of Short-Term Forecasting of Market Parameters for Portfolio Selection," Annals of Economics and Finance, Society for AEF, vol. 16(1), pages 143-161, May.
    7. Nikolai Dokuchaev, 2009. "Mutual Fund Theorem for continuous time markets with random coefficients," Papers 0911.3194, arXiv.org.
    8. David Feldman, 2007. "Incomplete information equilibria: Separation theorems and other myths," Annals of Operations Research, Springer, vol. 151(1), pages 119-149, April.
    9. Alexandra Rodkina & Nikolai Dokuchaev, 2014. "On asymptotic optimality of Merton's myopic portfolio strategies for discrete time market," Papers 1403.4329, arXiv.org, revised Nov 2014.
    10. Vikranth Lokeshwar Dhandapani & Shashi Jain, 2024. "Neural Networks for Portfolio-Level Risk Management: Portfolio Compression, Static Hedging, Counterparty Credit Risk Exposures and Impact on Capital Requirement," Papers 2402.17941, arXiv.org.

    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. Dokuchaev, Nikolai & Yu Zhou, Xun, 2001. "Optimal investment strategies with bounded risks, general utilities, and goal achieving," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 289-309, April.
    2. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    3. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    4. Timothy Johnson, 2015. "Reciprocity as a Foundation of Financial Economics," Journal of Business Ethics, Springer, vol. 131(1), pages 43-67, September.
    5. Marcos Escobar-Anel & Matt Davison & Yichen Zhu, 2022. "Derivatives-based portfolio decisions: an expected utility insight," Annals of Finance, Springer, vol. 18(2), pages 217-246, June.
    6. Carpenter, Jennifer N., 1998. "The exercise and valuation of executive stock options," Journal of Financial Economics, Elsevier, vol. 48(2), pages 127-158, May.
    7. Wolfgang Stummer, 2002. "Some Potential Means for Venture Valuation," Journal of Entrepreneurial Finance, Pepperdine University, Graziadio School of Business and Management, vol. 7(3), pages 39-52, Fall.
    8. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    9. Gómez-Valle, Lourdes & Marti­nez-Rodri­guez, Julia, 2008. "Modelling the term structure of interest rates: An efficient nonparametric approach," Journal of Banking & Finance, Elsevier, vol. 32(4), pages 614-623, April.
    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. Tenorio Villal¢n, Angel F. & Martín Caraballo, Ana M. & Paralera Morales, Concepción & Contreras Rubio, Ignacio, 2013. "Ecuaciones diferenciales y en diferencias aplicadas a los conceptos económicos y financieros || Differential and Difference Equations Applied to Economic and Financial Concepts," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 16(1), pages 165-199, December.
    12. Yang Shen, 2020. "Effect of Variance Swap in Hedging Volatility Risk," Risks, MDPI, vol. 8(3), pages 1-34, July.
    13. Francisco Venegas Martínez & Abigail Rodríguez Nava, 2009. "Consumo y decisiones de portafolio en ambientes estocásticos: un marco teórico unificador," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 29-64, November.
    14. Jianjun Miao & Neng Wang, 2004. "Investment, Hedging, and Consumption Smoothing," Finance 0407014, University Library of Munich, Germany.
    15. Venegas-Martínez, Francisco & Polanco-Gaytán, Mayrén (ed.), 2011. "Macroeconomía Estocástica," Sección de Estudios de Posgrado e Investigación de la Escuela Superios de Economía del Instituto Politécnico Nacional, Escuela Superior de Economía, Instituto Politécnico Nacional, edition 1, volume 1, number 005, July.
    16. Jimmy E. Hilliard & Jitka Hilliard, 2018. "Rebalancing versus buy and hold: theory, simulation and empirical analysis," Review of Quantitative Finance and Accounting, Springer, vol. 50(1), pages 1-32, January.
    17. Simon Ellersgaard & Martin Tegnér, 2018. "Stochastic volatility for utility maximizers — A martingale approach," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-39, March.
    18. Merton, Robert C., 1993. "On the microeconomic theory of investment under uncertainty," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 13, pages 601-669, Elsevier.
    19. Iyer, Sriya & Velu, Chander, 2006. "Real options and demographic decisions," Journal of Development Economics, Elsevier, vol. 80(1), pages 39-58, June.
    20. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "When Is Time Continuous?," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 3, pages 71-102, World Scientific Publishing Co. Pte. Ltd..

    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:math/0207260. 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.