Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing
This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies -- those strategies whose wealth process is a supermartingale under all pricing measures with finite relative entropy. We give necessary and sufficient conditions for the absence of utility-based arbitrage, and for the existence of a solution to the primal problem. We consider two utility-based methods which can be used to price contingent claims. Firstly we investigate marginal utility-based price processes (MUBPP's). We show that such processes can be characterized as local martingales under the normalized optimal dual measure for the utility maximizing investor. Finally, we present some new results on utility indifference prices, including continuity properties and volume asymptotics for the case of a general utility function, unbounded endowment and unbounded contingent claims.
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.:
- repec:dau:papers:123456789/342 is not listed on IDEAS
- Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293, arXiv.org.
- Gordan Zitkovic, 2005. "Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment," Papers math/0503516, arXiv.org.
- Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, August.
- Foldes, Lucien, 2000. "Valuation and martingale properties of shadow prices: An exposition," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1641-1701, October.
- Freddy Delbaen & Peter Grandits & Thorsten Rheinländer & Dominick Samperi & Martin Schweizer & Christophe Stricker, 2002. "Exponential Hedging and Entropic Penalties," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 99-123.
- Julien Hugonnier & Dmitry Kramkov & Walter Schachermayer, 2005. "On Utility-Based Pricing Of Contingent Claims In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 203-212.
- Jan Kallsen & Christoph Kühn, 2004. "Pricing derivatives of American and game type in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 261-284, May.
- Jan Kallsen, 2002. "Derivative pricing based on local utility maximization," Finance and Stochastics, Springer, vol. 6(1), pages 115-140.
- Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:0706.0478. 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: (arXiv administrators)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 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.