On the foundations of LÃ©vy finance. Equilibrium for a single-agent financial market with jumps
For a continuous-time financial market with a single agent, we establish equilibrium pricing formulae under the assumption that the dividends follow an exponential LÃ©vy 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 LÃ©vy process essentially only if this process is geometric Brownian motion.
|Date of creation:||15 Aug 2011|
|Date of revision:|
|Contact details of provider:|| Postal: Postfach 10 01 31, 33501 Bielefeld|
Web page: http://www.imw.uni-bielefeld.de/
More information through EDIRC
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.:
- Merton, Robert C., 1976.
"Option pricing when underlying stock returns are discontinuous,"
Journal of Financial Economics,
Elsevier, vol. 3(1-2), pages 125-144.
- Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- 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.
- Herzberg, Frederik, 2011. "Linear hyperfinite LÃ©vy integrals," Center for Mathematical Economics Working Papers 404, Center for Mathematical Economics, Bielefeld University.
- 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.
- Khan, A. & Sun, Y., 2000. "Asymptotic Arbitrage and the APT with or Without Measure-Theoretic Structures," Papiers d'Economie MathÃ©matique et Applications 2000.81, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- 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.
- 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.
- 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.
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)
If references are entirely missing, you can add them using this form.