"Itô's Lemma" and the Bellman equation: An applied view

Ken Sennewald and Klaus Wälde

No 04/05, Dresden Discussion Paper Series in Economics from Technische Universität Dresden, Faculty of Business and Economics, 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; Consump (search for similar items in EconPapers)
JEL-codes: C61 D81 D90 G11 (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:tuddps:0405

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