“Itô’s Lemma“ and the Bellman Equation for Poisson Processes: An Applied View

Ken Sennewald and Klaus Wälde

No 1684, CESifo Working Paper Series from CESifo

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.

Keywords: stochastic differential equation; Poisson process; Bellman equation; portfolio optimization; consumption optimization (search for similar items in EconPapers)
Date: 2006
New Economics Papers: this item is included in nep-fin and nep-upt
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Citations: View citations in EconPapers (10)

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Related works:
Journal Article: “Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View (2006)
Working Paper: "Ito's Lemma" and the Bellman equation for Poisson processes: An applied view (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:ces:ceswps:_1684

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