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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:2006
Series/Report no.:CESifo working papers 1684
Abstract:Using the Hamilton-Jacobi-Bellman equation, we derive both a Keynes-Ramsey rule and a closed form solution for an optimal consumption-investment problem with labor income. The utility function is unbounded and uncertainty stems from a Poisson process. Our results can be derived because of the proofs presented in the accompanying paper by Sennewald (2006). Additional examples are given which highlight the correct use of the Hamilton-Jacobi- Bellman equation and the change-of-variables formula (sometimes referred to as ?Ito?s- Lemma?) under Poisson uncertainty.
Subjects:stochastic differential equation
Poisson process
Bellman equation
portfolio optimization
consumption optimization
Document Type:Working Paper
Appears in Collections:CESifo Working Papers, CESifo Group Munich

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