"Ito's Lemma" and the Bellman equation for Poisson processes: An applied view

Arbeitspapier

Rare and randomly occurring events are important features of the economic world. In continuous time they can easily be modeled by Poisson processes. Analyzing optimal behavior in such a setup requires the appropriate version of the change of variables formula and the Hamilton-Jacobi-Bellman equation. This paper provides examples for the application of both tools in economic modeling. It accompanies the proofs in Sennewald (2005), who shows, under milder conditions than before, that the Hamilton-Jacobi-Bellman equation is both a necessary and sufficient criterion for optimality. The main example here consists of a consumption-investment problem with labor income. It is shown how the Hamilton-Jacobi-Bellman equation can be used to derive both a Keynes-Ramsey rule and a closed form solution. We also provide a new result.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: W.E.P. - Würzburg Economic Papers ; No. 58

Klassifikation und Themen

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

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Sennewald, Ken ; Wälde, Klaus
• Ereignis: Veröffentlichung
• (wer): University of Würzburg, Department of Economics
• (wo): Würzburg
• (wann): 2005

Weitere Informationen

• Handle: http://hdl.handle.net/10419/22352
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ