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Erscheinungsjahr: 
2006
Schriftenreihe/Nr.: 
CESifo Working Paper No. 1684
Verlag: 
Center for Economic Studies and ifo Institute (CESifo), Munich
Zusammenfassung: 
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.
Schlagwörter: 
stochastic differential equation
Poisson process
Bellman equation
portfolio optimization
consumption optimization
JEL: 
G11
D90
D81
C61
Dokumentart: 
Working Paper
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