“Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View
AbstractUsing 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 âItoâs-Lemmaâ) under Poisson uncertainty.
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Bibliographic InfoArticle provided by Springer in its journal Journal of Economics.
Volume (Year): 89 (2006)
Issue (Month): 1 (October)
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Web page: http://www.springerlink.com/link.asp?id=108909
stochastic differential equation; Poisson process; Bellman equation; portfolio optimization; consumption optimization; C61; D81; D90; G11;
Other versions of this item:
- Sennewald, Ken & Wälde, Klaus, 2005. ""Ito's Lemma" and the Bellman equation for Poisson processes: An applied view," W.E.P. - WÃ¼rzburg Economic Papers 58, University of Würzburg, Chair for Monetary Policy and International Economics.
- Ken Sennewald & Klaus Waelde, 2006. "“Itô’s Lemma“ and the Bellman Equation for Poisson Processes: An Applied View," CESifo Working Paper Series 1684, CESifo Group Munich.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- D90 - Microeconomics - - Intertemporal Choice and Growth - - - General
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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