IDEAS home Printed from
   My bibliography  Save this paper

On the foundations of Lévy finance. Equilibrium for a single-agent financial market with jumps


  • Herzberg, Frederik

    (Center for Mathematical Economics, Bielefeld University)


For a continuous-time financial market with a single agent, we establish equilibrium pricing formulae under the assumption that the dividends follow an exponential Lévy process. The agent is allowed to consume a lump at the terminal date; before, only flow consumption is allowed. The agent's utility function is assumed to be additive, defined via strictly increasing, strictly concave smooth felicity functions which are bounded below (thus, many CRRA and CARA utility functions are included). For technical reasons we require that only pathwise continuous trading strategies are permitted in the demand set. The resulting equilibrium prices depend on the agent's risk-aversion through the felicity functions. It turns out that these prices will be the (stochastic) exponential of a Lévy process essentially only if this process is geometric Brownian motion.

Suggested Citation

  • Herzberg, Frederik, 2011. "On the foundations of Lévy finance. Equilibrium for a single-agent financial market with jumps," Center for Mathematical Economics Working Papers 406, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:406

    Download full text from publisher

    File URL:
    File Function: First Version, 2008
    Download Restriction: no

    References listed on IDEAS

    1. Nigel J. Cutland & Ekkehard Kopp & Walter Willinger, 1993. "From Discrete to Continuous Financial Models: New Convergence Results For Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 101-123.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. Khan, M. Ali & Sun, Yeneng, 2001. "Asymptotic Arbitrage and the APT with or without Measure-Theoretic Structures," Journal of Economic Theory, Elsevier, vol. 101(1), pages 222-251, November.
    4. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics,in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
    5. Bick, Avi, 1990. " On Viable Diffusion Price Processes of the Market Portfolio," Journal of Finance, American Finance Association, vol. 45(2), pages 673-689, June.
    6. Herzberg, Frederik, 2011. "Linear hyperfinite Lévy integrals," Center for Mathematical Economics Working Papers 404, Center for Mathematical Economics, Bielefeld University.
    7. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Asset pricing; Financial equilibrium; Lévy processes; Representative agent models; Nonstandard analysis;

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:bie:wpaper:406. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Bettina Weingarten). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.