"Ito's Lemma" and the Bellman equation for Poisson processes: An applied view
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.
|Date of creation:||2005|
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- Sennewald, Ken, 2005. "Controlled Stochastic Differential Equations under Poisson Uncertainty and with Unbounded Utility," Dresden Discussion Paper Series in Economics 03/05, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
- Maurice Obstfeld, 1992.
"Risk-taking, global diversification, and growth,"
Discussion Paper / Institute for Empirical Macroeconomics
61, Federal Reserve Bank of Minneapolis.
- Obstfeld, Maurice, 1993. "Risk-Taking, Global Diversification, and Growth," Center for International and Development Economics Research (CIDER) Working Papers 233197, University of California-Berkeley, Department of Economics.
- Maurice Obstfeld, 1992. "Risk-Taking, Global Diversification, and Growth," NBER Working Papers 4093, National Bureau of Economic Research, Inc.
- 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.
- Obstfeld, Maurice, 1992. "Risk-Taking, Global Diversification, and Growth," CEPR Discussion Papers 688, C.E.P.R. Discussion Papers.
- Grossman, G.M. & Helpman, E., 1989.
"Quality Ledders In The Theory Of Growth,"
148, Princeton, Woodrow Wilson School - Public and International Affairs.
- 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.
- Chang,Fwu-Ranq, 2004.
"Stochastic Optimization in Continuous Time,"
Cambridge University Press, number 9780521834063, May.
- 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 247-257, August.
- 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.
- Walde, Klaus, 1999. "A Model of Creative Destruction with Undiversifiable Risk and Optimising Households," Economic Journal, Royal Economic Society, vol. 109(454), pages 156-171, March.
- Tjalling C. Koopmans, 1963. "On the Concept of Optimal Economic Growth," Cowles Foundation Discussion Papers 163, Cowles Foundation for Research in Economics, Yale University.
- Philippe Aghion & Peter Howitt, 1990.
"A Model of Growth Through Creative Destruction,"
NBER Working Papers
3223, National Bureau of Economic Research, Inc.
- Aghion, P. & Howitt, P., 1990. "A Model Of Growth Through Creative Destruction," DELTA Working Papers 90-12, DELTA (Ecole normale supérieure).
- Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth Through Creative Destruction," Scholarly Articles 12490578, Harvard University Department of Economics.
- 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.
- Aghion, P. & Howitt, P., 1989. "A Model Of Growth Through Creative Destruction," Working papers 527, Massachusetts Institute of Technology (MIT), 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.
- A. Sandmo, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Oxford University Press, vol. 37(3), pages 353-360.
- Marco Scarsini & Bruno Bassan & Erhan Cinlare, 1993.
"Stochastic comparisons of Itô processes,"
- Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March.
- Walde, Klaus, 1999. "Optimal Saving under Poisson Uncertainty," Journal of Economic Theory, Elsevier, vol. 87(1), pages 194-217, July.
- Moen, Espen R, 1997.
"Competitive Search Equilibrium,"
Journal of Political Economy,
University of Chicago Press, vol. 105(2), pages 385-411, April.
- Aase, Knut Kristian, 1984. "Optimum portfolio diversification in a general continuous-time model," Stochastic Processes and their Applications, Elsevier, vol. 18(1), pages 81-98, September.
- R. C. Merton, 1970.
"Optimum Consumption and Portfolio Rules in a Continuous-time Model,"
58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
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