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- Title
“Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View.
- Authors
Sennewald, Ken; Wälde, Klaus
- 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 ``Itô's Lemma'') under Poisson uncertainty.
- Subjects
POISSON processes; HAMILTON-Jacobi equations; UTILITY functions; STOCHASTIC differential equations; CONSUMPTION (Economics); INVESTMENTS; PORTFOLIO performance
- Publication
Journal of Economics, 2006, Vol 89, Issue 1, p1
- ISSN
0931-8658
- Publication type
Article
- DOI
10.1007/s00712-006-0203-9