"Ito's Lemma" and the Bellman equation for Poisson processes: An applied view
AbstractRare 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. --
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Bibliographic InfoPaper provided by University of Würzburg, Chair for Monetary Policy and International Economics in its series W.E.P. - Würzburg Economic Papers with number 58.
Date of creation: 2005
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Stochastic differential equation; Poisson process; Bellman equation; Portfolio optimization; Consumption optimization;
Other versions of this item:
- Ken Sennewald & Klaus Wälde, 2006. "“Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View," Journal of Economics, Springer, vol. 89(1), pages 1-36, October.
- 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 - - - General
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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