“Itô’s Lemma“ and the Bellman Equation for Poisson Processes: An Applied View

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“Itô’s Lemma“ and the Bellman Equation for Poisson Processes: An Applied View

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Ken Sennewald ()
Klaus Wälde ()

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Klaus Wälde

Abstract

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.

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Paper provided by CESifo GmbH in its series CESifo Working Paper Series with number CESifo Working Paper No. 1684.

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Date of creation: 2006
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Handle: RePEc:ces:ceswps:_1684

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Article
- 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. [Downloadable!] (restricted)

Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
D90 - Microeconomics - - Intertemporal Choice and Growth - - - General
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

This paper has been announced in the following NEP Reports:

NEP-ALL-2006-04-08 (All new papers)
NEP-FIN-2006-04-08 (Finance)
NEP-UPT-2006-04-08 (Utility Models & Prospect Theory)

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Obstfeld, Maurice, 1994. "Risk-Taking, Global Diversification, and Growth," American Economic Review, American Economic Association, vol. 84(5), pages 1310-29, December. [Downloadable!] (restricted)
Other versions:
- Maurice Obstfeld, 1992. "Risk-taking, global diversification, and growth," Discussion Paper / Institute for Empirical Macroeconomics 61, Federal Reserve Bank of Minneapolis. [Downloadable!]
- Obstfeld, Maurice, 1992. "Risk-Taking, Global Diversification, and Growth," CEPR Discussion Papers 688, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
- Maurice Obstfeld., 1993. "Risk-Taking, Global Diversification, and Growth," Center for International and Development Economics Research (CIDER) Working Papers C93-016, University of California at Berkeley.
- Maurice Obstfeld, 1995. "Risk-Taking, Global Diversification, and Growth," NBER Working Papers 4093, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
Sandmo, Agnar, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Blackwell Publishing, vol. 37(3), pages 353-60, July. [Downloadable!] (restricted)
Moen, Espen R, 1997. "Competitive Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 385-411, April.
Other versions:
- Moen, E.R., 1995. "Competitive Search Equilibrium," Memorandum 37/1995, Oslo University, Department of Economics.
Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May. [Downloadable!] (restricted)
Kiyotaki, Nobuhiro & Wright, Randall, 1991. "A contribution to the pure theory of money," Journal of Economic Theory, Elsevier, vol. 53(2), pages 215-235, April. [Downloadable!] (restricted)
Other versions:
- Nobuhiro Kiyotaki & Randall Wright, 1989. "A contribution to the pure theory of money," Staff Report 123, Federal Reserve Bank of Minneapolis. [Downloadable!]
Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March. [Downloadable!] (restricted)
Framstad, Nils Chr. & Oksendal, Bernt & Sulem, Agnes, 2001. "Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 233-257, April. [Downloadable!] (restricted)
Gene M. Grossman & Elhanan Helpman, 1991. "Quality Ladders in the Theory of Growth," NBER Working Papers 3099, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
Other versions:
- Grossman, G.M. & Helpman, E., 1989. "Quality Ledders In The Theory Of Growth," Papers 148, Princeton, Woodrow Wilson School - Public and International Affairs.
- Grossman, Gene M & Helpman, Elhanan, 1991. "Quality Ladders in the Theory of Growth," Review of Economic Studies, Blackwell Publishing, vol. 58(1), pages 43-61, January. [Downloadable!] (restricted)
Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-51, March. [Downloadable!] (restricted)
Other versions:
- Aghion, P. & Howitt, P., 1990. "A Model Of Growth Through Creative Destruction," DELTA Working Papers 90-12, DELTA (Ecole normale supérieure).
- Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," UWO Department of Economics Working Papers 8904, University of Western Ontario, Department of Economics.
- Philippe Aghion & Peter Howitt, 1990. "A Model of Growth Through Creative Destruction," NBER Working Papers 3223, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
- Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," Working papers 527, Massachusetts Institute of Technology (MIT), Department of Economics.
Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August. [Downloadable!] (restricted)

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