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ifo Institut – Leibniz-Institut für Wirtschaftsforschung an der Universität München >
CESifo Working Papers, CESifo Group Munich >
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http://hdl.handle.net/10419/19148
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| Title: | | "Ito's Lemma" and the Bellman equation for poisson processes : an applied view  |
| 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 |
| JEL: | | G11 D90 D81 C61 |
| Document Type: | | Working Paper |
| Appears in Collections: | | CESifo Working Papers, CESifo Group Munich
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