"Ito's Lemma" and the Bellman equation for poisson processes : an applied view

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: CESifo Working Paper ; No. 1684

Classification and Topics

• Classification: Wirtschaft ; Portfolio Choice; Investment Decisions ; Micro-Based Behavioral Economics: General‡ ; Criteria for Decision-Making under Risk and Uncertainty ; Optimization Techniques; Programming Models; Dynamic Analysis
• Subject: stochastic differential equation ; Poisson process ; Bellman equation ; portfolio optimization ; consumption optimization ; Portfolio-Management ; Zeitpräferenz ; Analysis ; Stochastischer Prozess ; Theorie ; Stochastische Differentialgleichung

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Sennewald, Ken ; Wälde, Klaus
• Event: Veröffentlichung
• (who): Center for Economic Studies and ifo Institute (CESifo)
• (where): Munich
• (when): 2006

Further information

• Handle: http://hdl.handle.net/10419/19148
• Last update: 10.03.2025, 11:45 AM CET