"Ito's Lemma" and the Bellman equation for Poisson processes: An applied view

Ken Sennewald and Klaus Wälde

No 58, W.E.P. - Würzburg Economic Papers from University of Würzburg, Department of Economics

Abstract: 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.

Keywords: Stochastic differential equation; Poisson process; Bellman equation; Portfolio optimization; Consumption optimization (search for similar items in EconPapers)
JEL-codes: C61 D81 D90 G11 (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/22352/1/wep58.pdf (application/pdf)

Related works:
Journal Article: “Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View (2006)
Working Paper: “Itô’s Lemma“ and the Bellman Equation for Poisson Processes: An Applied View (2006)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zbw:wuewep:58

Access Statistics for this paper

More papers in W.E.P. - Würzburg Economic Papers from University of Würzburg, Department of Economics Contact information at EDIRC.
Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics ().