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Title:"Ito's Lemma" and the Bellman equation for Poisson processes: An applied view PDF Logo
Authors:Sennewald, Ken
Wälde, Klaus
Issue Date:2005
Series/Report no.:Würzburg economic papers 58
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.
Subjects:Stochastic differential equation
Poisson process
Bellman equation
Portfolio optimization
Consumption optimization
JEL:C61
G11
D90
D81
Document Type:Working Paper
Appears in Collections:W.E.P. - Würzburg Economic Papers, Lst. f. VWL, Geld u. internat. Wirtschaftsbeziehungen, Universität Würzburg

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