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

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Author Info
Frederik Herzberg () (Institute of Mathematical Economics, Bielefeld University)

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Abstract

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.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-406.pdf
File Format: application/pdf
File Function: First version, 2008
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Publisher Info
Paper provided by Bielefeld University, Institute of Mathematical Economics in its series Working Papers with number 406.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 23 pages
Date of creation: Sep 2008
Date of revision:
Handle: RePEc:bie:wpaper:406

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Postal: Postfach 10 01 31, 33501 Bielefeld
Web page: http://www.imw.uni-bielefeld.de/
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For technical questions regarding this item, or to correct its listing, contact: (Dr. Frederik Herzberg).

Related research
Keywords: financial equilibrium; asset pricing; representative agent models; Lévy processes; nonstandard analysis;

Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Bick, Avi, 1990. " On Viable Diffusion Price Processes of the Market Portfolio," Journal of Finance, American Finance Association, vol. 45(2), pages 673-89, June. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
    Other versions:
  3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
    Other versions:
  4. 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 363-84, March. [Downloadable!] (restricted)
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