IDEAS home Printed from https://ideas.repec.org/p/hhs/hastef/0122.html
   My bibliography  Save this paper

Diversified Portfolios in Continuous Time

Author

Listed:
  • Björk, Tomas

    (Department of Finance)

  • Näslund, Bertil

    (Department of Finance)

Abstract

We study a financial market containing an infinite number of assets, where each asset price is driven by an idiosyncratic random source as well as by a systematic noise term. Introducing 2 asymptotic assets" which correspond to certain infinitely well diversified portfolios we study absence of (asymptotic) arbiytrage, and in this context we obtain continuous time extensions of atemporal APT results. We also study completeness and derivative pricing, showing that the possibility of forming infinitely well diversified portfolios has the property of completing the market. It also turns out that models where the all risk is of diffusion type are qualitatively quite different from models where one risk is of diffusion type and the other is of Poisson type. We also present a simple martingale based theory for absence of asymptotic arbitrage.

Suggested Citation

  • Björk, Tomas & Näslund, Bertil, 1996. "Diversified Portfolios in Continuous Time," SSE/EFI Working Paper Series in Economics and Finance 122, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0122
    as

    Download full text from publisher

    File URL: http://swopec.hhs.se/hastef/papers/hastef0122.pdf
    File Function: Complete Rendering
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    2. Philippe Artzner & Freddy Delbaen, 1995. "Default Risk Insurance And Incomplete Markets1," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 187-195, July.
    3. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239, April.
    4. Chamberlain, Gary, 1988. "Asset Pricing in Multiperiod Securities Markets," Econometrica, Econometric Society, vol. 56(6), pages 1283-1300, November.
    5. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    6. Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
    7. Gur Huberman, 2005. "A Simple Approach to Arbitrage Pricing Theory," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 9, pages 289-308, World Scientific Publishing Co. Pte. Ltd..
    8. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
    9. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    10. Reisman, Haim, 1992. "Intertemporal Arbitrage Pricing Theory," Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 105-122.
    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. Erdinc Akyildirim & Frank J. Fabozzi & Ahmet Goncu & Ahmet Sensoy, 2022. "Statistical arbitrage in jump-diffusion models with compound Poisson processes," Annals of Operations Research, Springer, vol. 313(2), pages 1357-1371, June.
    2. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
    3. Lim Kian Guan & Liu Xiaoqing & Tsui Kai Chong, 2004. "Asymptotic dynamics and value-at-risk of large diversified portfolios in a jump-diffusion market," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 129-139.

    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. 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.
    2. Nawalkha, Sanjay K., 1997. "A multibeta representation theorem for linear asset pricing theories," Journal of Financial Economics, Elsevier, vol. 46(3), pages 357-381, December.
    3. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2005.
    4. Kraft, Holger & Steffensen, Mogens, 2008. "How to invest optimally in corporate bonds: A reduced-form approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 348-385, February.
    5. Chenghu Ma, 2003. "Term Structure of Interest Rates in the Presence of Levy Jumps: The HJM Approach," Annals of Economics and Finance, Society for AEF, vol. 4(2), pages 401-426, November.
    6. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011.
    7. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6, July-Dece.
    8. Wolfgang Drobetz & Dirk Schilling & Lars Tegtmeier, 2010. "Common risk factors in the returns of shipping stocks," Maritime Policy & Management, Taylor & Francis Journals, vol. 37(2), pages 93-120, March.
    9. repec:dau:papers:123456789/5374 is not listed on IDEAS
    10. Zhang, Chu, 2009. "On the explanatory power of firm-specific variables in cross-sections of expected returns," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 306-317, March.
    11. Colin T. Bowers & Chris Heaton, 2013. "What does high-dimensional factor analysis tell us about risk factors in the Australian stock market?," Applied Economics, Taylor & Francis Journals, vol. 45(11), pages 1395-1404, April.
    12. Robert A. Jarrow, 1999. "In Honor of the Nobel Laureates Robert C. Merton and Myron S. Scholes: A Partial Differential Equation That Changed the World," Journal of Economic Perspectives, American Economic Association, vol. 13(4), pages 229-248, Fall.
    13. Chen, Cho-Jieh & Panjer, Harry, 2003. "Unifying discrete structural models and reduced-form models in credit risk using a jump-diffusion process," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 357-380, October.
    14. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    15. Colino, Jesús P. & Stute, Winfried, 2008. "Credit risk with semimartingales and risk-neutrality," DES - Working Papers. Statistics and Econometrics. WS ws085417, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Zaevski, Tsvetelin S. & Kounchev, Ognyan & Savov, Mladen, 2019. "Two frameworks for pricing defaultable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 309-319.
    17. Munk, Claus, 2015. "Financial Asset Pricing Theory," OUP Catalogue, Oxford University Press, number 9780198716457, Decembrie.
    18. Tahir Choulli & Catherine Daveloose & Michèle Vanmaele, 2020. "A martingale representation theorem and valuation of defaultable securities," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1527-1564, October.
    19. Bruno Feunou & Jean-Sébastien Fontaine & Abderrahim Taamouti & Roméo Tédongap, 2014. "Risk Premium, Variance Premium, and the Maturity Structure of Uncertainty," Review of Finance, European Finance Association, vol. 18(1), pages 219-269.
    20. Li, Yuming, 1998. "Expected stock returns, risk premiums and volatilities of economic factors1," Journal of Empirical Finance, Elsevier, vol. 5(2), pages 69-97, June.
    21. Pringles, Rolando & Olsina, Fernando & Penizzotto, Franco, 2020. "Valuation of defer and relocation options in photovoltaic generation investments by a stochastic simulation-based method," Renewable Energy, Elsevier, vol. 151(C), pages 846-864.

    More about this item

    Keywords

    Large economies; diversifiable risk; APT; asymptotic arbitrage; completeness; martingales;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:hhs:hastef:0122. 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: Helena Lundin (email available below). General contact details of provider: https://edirc.repec.org/data/erhhsse.html .

    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.