"Itô's Lemma" and the Bellman equation: An applied view
Rare and randomly occurring events are important features of the economic world. In continuous time they can easily be modeled by Poisson processes. Analyzing optimal behavior in such a setup requires the appropriate version of the change of variables formula and the Hamilton-Jacobi-Bellman equation. This paper provides examples for the application of both tools in economic modeling. It accompanies the proofs in Sennewald (2005), who shows, under milder conditions than before, that the Hamilton-Jacobi-Bellman equation is both a necessary and sufficient criterion for optimality. The main example here consists of a consumption-investment problem with labor income. It is shown how the Hamilton-Jacobi-Bellman equation can be used to derive both a Keynes-Ramsey rule and a closed form solution. We also provide a new result.
|Date of creation:||2005|
|Date of revision:|
|Contact details of provider:|| Postal: 01062 Dresden|
Phone: ++49 351 463 2196
Fax: ++49 351 463 7739
Web page: http://www.tu-dresden.de/wiwi/
More information through EDIRC
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.:
- Aghion, P. & Howitt, P., 1989.
"A Model Of Growth Through Creative Destruction,"
527, Massachusetts Institute of Technology (MIT), Department of Economics.
- Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth Through Creative Destruction," Scholarly Articles 12490578, Harvard University Department of Economics.
- Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," UWO Department of Economics Working Papers 8904, University of Western Ontario, Department of Economics.
- Aghion, P. & Howitt, P., 1990. "A Model Of Growth Through Creative Destruction," DELTA Working Papers 90-12, DELTA (Ecole normale supérieure).
- Philippe Aghion & Peter Howitt, 1990. "A Model of Growth Through Creative Destruction," NBER Working Papers 3223, National Bureau of Economic Research, Inc.
- Gene M. Grossman & Elhanan Helpman, 1989.
"Quality Ladders in the Theory of Growth,"
NBER Working Papers
3099, National Bureau of Economic Research, Inc.
- Kiyotaki, Nobuhiro & Wright, Randall, 1991.
"A contribution to the pure theory of money,"
Journal of Economic Theory,
Elsevier, vol. 53(2), pages 215-235, April.
- Moen, Espen R, 1997.
"Competitive Search Equilibrium,"
Journal of Political Economy,
University of Chicago Press, vol. 105(2), pages 385-411, April.
- Aase, Knut Kristian, 1984. "Optimum portfolio diversification in a general continuous-time model," Stochastic Processes and their Applications, Elsevier, vol. 18(1), pages 81-98, September.
- Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March.
- Walde, Klaus, 1999. "A Model of Creative Destruction with Undiversifiable Risk and Optimising Households," Economic Journal, Royal Economic Society, vol. 109(454), pages C156-71, March.
- Walde, Klaus, 1999. "Optimal Saving under Poisson Uncertainty," Journal of Economic Theory, Elsevier, vol. 87(1), pages 194-217, July.
- Sennewald, Ken, 2005. "Controlled Stochastic Differential Equations under Poisson Uncertainty and with Unbounded Utility," Dresden Discussion Paper Series in Economics 03/05, Dresden University of Technology, Faculty of Business and Economics, Department of Economics.
- Framstad, Nils Chr. & Oksendal, Bernt & Sulem, Agnes, 2001. "Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 233-257, April.
- Merton, Robert C., 1971.
"Optimum consumption and portfolio rules in a continuous-time model,"
Journal of Economic Theory,
Elsevier, vol. 3(4), pages 373-413, December.
- R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
When requesting a correction, please mention this item's handle: RePEc:zbw:tuddps:0405. 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: (ZBW - German National Library of Economics)
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.