Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs
We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we reformulate and reduce the Hamilton-Jacobi-Bellman equation for this singular stochastic control problem to a non-standard free-boundary problem for a first-order ODE with an integral constraint. Having shown that the free boundary problem has a smooth solution, we use it to construct the solution of the original optimal investment/consumption problem in a self-contained manner and without any recourse to the dynamic programming principle. Furthermore, we provide an explicit characterization of model parameters for which the value function is finite.
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:123456789/5630 is not listed on IDEAS
- repec:crs:wpaper:9513 is not listed on IDEAS
- Elyès Jouini & Hedi Kallal, 1995. "Martingale and Arbitrage in securities markets with transaction cost," Post-Print halshs-00167138, HAL.
- J. Kallsen & J. Muhle-Karbe, 2010. "On using shadow prices in portfolio optimization with transaction costs," Papers 1010.4989, arXiv.org.
- Victor Ginsburgh & Michiel Keyzer, 2002.
"The Structure of Applied General Equilibrium Models,"
MIT Press Books,
The MIT Press,
edition 1, volume 1, number 0262571579, July.
- Victor Ginsburgh & Michiel Keyzer, 1997. "The structure of applied general equilibrium models," ULB Institutional Repository 2013/1653, ULB -- Universite Libre de Bruxelles.
- Victor Ginsburgh & Michiel Keyzer, 2002. "The structure of applied general equilibrium models," ULB Institutional Repository 2013/3313, ULB -- Universite Libre de Bruxelles.
- Lamberton, Damien & Pham, Huyên & Schweizer, Martin, 1998. "Local risk-minimization under transaction costs," SFB 373 Discussion Papers 1998,18, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
- Damien Lamberton & Huyên Pham & Martin Schweizer, 1998. "Local Risk-Minimization Under Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 585-612, August.
- Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1204.0305. 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.