We show how the theorems of monotone and bounded convergence can be used to interchange expectation and integral in Es
R∞
s e−ρs(t)(t−s)Zts,xdt. At first, we consider the expectation of the finite horizon integralRT
s e−ρs(t)(t−s)Zts,xdt. Here, in analogy to appendix B and with the upper bound (T − s) ZTs,x, the theorem of bounded conver-gence yields together with (30)
Es the theorem of monotone convergence tells us that R∞
s e−ρs(t)(t−s)Zts,xdt possess finite
References
Aase, K. K. (1984): “Optimum Portfolio Diversification in a General Continuous-Time Model,” Stochastic Processes and their Applications, 18, 81—98.
Bassan, B., E. Çinlar, and M. Scarsini (1993): “Stochastic Comparisons of Itô Processes,” Stochastic Processes and their Applications, 45, 1—11.
Bellamy, N. (2001): “Wealth Optimization in an Incomplete Market Driven by a Jump-Diffusion Process,” Journal of Mathematical Economics, 35, 259—287.
Browder, A. (1996): Mathematical Analysis. Springer, New York.
Crandall, M. G., H. Ishi, and P.-L. Lions (1992): “A User’s Guide to Viscosity Solutions of Second Order Partial Differential Equations,” Bull. Am. Math. Soc., 27, 1—67.
Crandall, M. G., and P.-L. Lions (1983): “Viscosity Solutions of Hamilton-Jacobi Equations,” Trans. Amer. Math. Soc., 277, 1—42.
Davis, M. H. A. (1993): Markov Models and Optimization. Chapman&Hall, London.
Dempster, M. A. H. (1991): “Optimal Control of Piecewise Deterministic Markov Processes,” in Applied Stochastic Analysis, ed. by M. H. A. Davis,andR. J. Elliott, pp. 303—325. Gordon and Breach, New York.
Dixit, A. K.,andR. S. Pindyck (1994): Investment Under Uncertainty. Princeton University Press, Princeton.
Duffie, D. (1992): Dynamic Asset Pricing Theory. Princeton Univ. Press, Prince-ton.
Fleming, W. H., and H. M. Soner (1993): Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York.
Framstad, N. C., B. Øksendal, and A. Sulem (2001): “Optimal Consumption and Portfolio in a Jump Diffusion Market with Proportional Transaction Costs,”
Journal of Mathematical Economics, 35, 233—257.
García, M. A., and R. J. Griego (1994): “An Elementary Theory of Stochastic Differential Equations Driven by A Poisson Process,” Commun. Statist. - Stochastic Models, 10(2), 335—363.
Gihman, I. I., and A. V. Skorohod (1972): Stochastic Differential Equations.
Springer-Verlag, New York.
Grossman, G., and E. Helpman (1991): “Quality Ladders in the Theory of Growth,” Review of Economic Studies, 58, 43—61.
Howitt, P. (1999): “Steady Endogenous Growth with Population and R&D Inputs Growing,” Journal of Political Economy, 107(4), 715—730.
Kamihigashi, T. (2001): “Necessity of Transversality Conditions for Infinite Time Horizons,” Econometrica, 69, 995—1012.
Kushner, H. J. (1967): Stochastic Stability and Control. Academic Press, London.
Kushner, H. J., and P. G. Dupuis (1992): Numerical Methods for Stochastic Control Problems in Continuous Time. Springer-Verlag, New York.
Le Van, C., and L. Morhaim (2002): “Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach,” Journal of Economic Theory, 105, 158—187.
Malliaris, A. G., and W. A. Brock (1982): Stochastic Methods in Economics and Finance. North-Holland, Amsterdam.
Merton, R. C. (1971): “Optimum Consumption and Portfolio Rules in a Continuous-Time Model,” Journal of Economic Theory, 3, 373—413.
Michel, P. (1982): “On the Transversality Condition in Infinite Horizon Optimal Problems,” Econometrica, 50, 975—985.
Moen, E. (1997): “Competitive Search Equilibrium,” Journal of Political Economy, 105, 385—411.
Øksendal, B. (2000): Stochastic Differential Equations. Springer-Verlag, Berlin.
Postel-Vinay, F. (2002): “The Dynamics of Technological Unemployment,” Inter-national Economic Review, 43, 737—760.
Protter, P. (1995): Stochastic Integration and Differential Equations. Springer-Verlag, Berlin.
Rincón-Zapatero, J. P., and C. Rodriguez-Palmero (2003): “Existence and Uniqueness of Solution to the Bellman Equation in the Unbounded Case,” Econo-metrica, 71, 1519—1555.
Segerstrom, P. (1998): “Endogenous Growth without Scale Effects,” American Economic Review, 88(5), 1290—1310.
Sennewald, K.,andK. Wälde (2005): “"Itô’s Lemma" and the Bellman Equation for Poisson Processes: An Applied View,” Dresden Discussion Paper Series in Economics.
Steger, T. M. (2005): “Stochastic Growth under Wiener and Poisson Uncertainty,”
Economic Letters, forthcoming.
Turnovsky, S. J. (1999): Methods of Macroeconomic Dynamics. MIT Press, Came-bridge, Massachusetts.
van Dijk, N. M. (1988): “On the Finite Horizon Bellman Equation for Controlled Markov Jump Models with Unbounded Characteristics: Existence and Approxi-mation,” Stochastic Processes and their Applications, 28, 141—157.
Wälde, K. (1999): “Optimal Saving under Poisson Uncertainty,” Journal of Eco-nomic Theory, 87, 194—217.
Wälde, K. (2005): “Endogenous Growth Cycles,” International Economic Review, forthcoming.
Dresden Discussion Paper Series in Economics
10/03 Berlemann, Michael: The Effect of Signalling and Beliefs on the Voluntary Provision of Public Goods - Some Experimental Evidence
11/03 Berlemann, Michael / Nenovsky, Nikolay: Lending of First Versus Lending of Last Resort - The Bulgarian Financial Crisis of 1996/1997
12/03 Wälde, Klaus: Endogenous business cycles and growth
13/03 Choi, Jay Pil / Thum, Marcel: The economics of repeated extortion
14/03 Broll, Udo / Eckwert, Bernhard: Transparency in the Foreign Exchange Market and the Volume of International Trade
15/03 Graff, Michael / Karmann, Alexander: What Determines the Finance-Growth Nexus?
An Endogenous Growth Model and Empirical Evidence
16/03 Steinmann, Lukas / Dittrich, Gunnar / Karmann, Alexander / Zweifel, Peter: Measuring and Comparing the (In)Efficiency of German and Swiss Hospitals
17/03 Lehmann-Waffenschmidt, Marco / Reina, Livia: Coalition formation in multilateral negotiations with a potential for logrolling: an experimental analysis of negotiators’ cognition processes
18/03 Lehmann-Waffenschmidt, Marco / Böhmer, Robert: Mentality Matters – Thorstein Veblens
‚Regime of Status‘ und Max Webers ‚Protestantische Ethik‘ aus der Sicht des (radikalen) Konstruktivismus. Eine Anwendung auf die ökonomischen Probleme des deutschen Wiedervereinigungsprozesses
19/03 Eisenschmidt, Jens / Wälde, Klaus: International Trade, Hedging and the Demand for Forward Contracts
20/03 Broll, Udo / Wong, Kit Pong: Capital Structure and the Firm under Uncertainty
01/04 Lehmann-Waffenschmidt, Marco: A Note on Continuously Decomposed Evolving Exchange Economies
02/04 Friedrich, B. Cornelia: Competition and the Evolution of Market Structure in the E-conomy.
03/04 Berlemann, Michael / Dittrich, Marcus / Markwardt, Gunther: The Value of Non-Binding Announcements in Public Goods Experiments. Some Theory and Experimental Evidence
04/04 Blum, Ulrich / Schaller, Armin / Veltins, Michael: The East German Cement Cartel: An Inquiry into Comparable Markets, Industry Structure, and Antitrust Policy
05/04 Schlegel, Christoph: Analytical and Numerical Solution of a Poisson RBC model 06/04 Lehmann-Waffenschmidt, Marco: Die ökonomische Botschaft in Goethes „Faust“
07/04 Fuchs, Michaela / Thum, Marcel: EU Enlargement: Challenges for Germany's New Laender 08/04 Seitz, Helmut: Implikationen der demographischen Veränderungen für die öffentlichen Haushalte
und Verwaltungen
09/04 Sülzle, Kai: Duopolistic Competition between Independent and Collaborative Business-to-Business Marketplaces
10/04 Broll, Udo / Eckwert, Bernhard: Transparency in the Interbank Market and the Volume of Bank Intermediated Loans
11/04 Thum, Marcel: Korruption
12/04 Broll, Udo / Hansen, Sabine / Marjit, Sugata: Domestic labor, foreign capital and national welfare 13/04 Nyamtseren, Lhamsuren: Challenges and Opportunities of Small Countries for Integration into the
Global Economy, as a Case of Mongolia
01/05 Schubert, Stefan / Broll, Udo: Dynamic Hedging of Real Wealth Risk
02/05 Günther, Edeltraud / Lehmann-Waffenschmidt, Marco: Deceleration - Revealed Preference in Society and Win-Win-Strategy for Sustainable Management. Concept and Exprimental Evidence