IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v116y2006i11p1530-1562.html
   My bibliography  Save this article

Verification theorems for stochastic optimal control problems via a time dependent Fukushima-Dirichlet decomposition

Author

Listed:
  • Gozzi, Fausto
  • Russo, Francesco

Abstract

This paper is devoted to presenting a method of proving verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term. The value function is assumed to be continuous in time and once differentiable in the space variable (C0,1) instead of once differentiable in time and twice in space (C1,2), like in the classical results. The results are obtained using a time dependent Fukushima-Dirichlet decomposition proved in a companion paper by the same authors using stochastic calculus via regularization. Applications, examples and a comparison with other similar results are also given.

Suggested Citation

  • Gozzi, Fausto & Russo, Francesco, 2006. "Verification theorems for stochastic optimal control problems via a time dependent Fukushima-Dirichlet decomposition," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1530-1562, November.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:11:p:1530-1562
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(06)00050-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, November.
    2. Lejay, Antoine, 2004. "A probabilistic representation of the solution of some quasi-linear PDE with a divergence form operator. Application to existence of weak solutions of FBSDE," Stochastic Processes and their Applications, Elsevier, vol. 110(1), pages 145-176, March.
    3. Luca Grosset & Bruno Viscolani, 2004. "Advertising for a new product introduction: A stochastic approach," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 149-167, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fabbri, Giorgio & Russo, Francesco, 2017. "Infinite dimensional weak Dirichlet processes and convolution type processes," Stochastic Processes and their Applications, Elsevier, vol. 127(1), pages 325-357.
    2. Fabbri, G. & Russo, F., 2017. "HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition," Working Papers 2017-07, Grenoble Applied Economics Laboratory (GAEL).
    3. Huberts, N.F.D. & Dawid, H. & Huisman, K.J.M. & Kort, P.M., 2019. "Entry deterrence by timing rather than overinvestment in a strategic real options framework," European Journal of Operational Research, Elsevier, vol. 274(1), pages 165-185.
    4. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    5. Anna Battauz & Marzia Donno & Alessandro Sbuelz, 2017. "Reaching nirvana with a defaultable asset?," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 31-52, November.
    6. Cristina Girolami & Giorgio Fabbri & Francesco Russo, 2014. "The covariation for Banach space valued processes and applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(1), pages 51-104, January.
    7. Bandini, Elena & Russo, Francesco, 2017. "Weak Dirichlet processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 4139-4189.
    8. Huberts, Nick F.D. & Rossi Silveira, Rafael, 2023. "How economic depreciation shapes the relationship of uncertainty with investments’ size & timing," International Journal of Production Economics, Elsevier, vol. 260(C).
    9. Giorgio Fabbri & Francesco Russo, 2016. "Infinite Dimensional Weak Dirichlet Processes and Convolution Type Processes," Working Papers halshs-01309384, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pablo D. Fajgelbaum & Edouard Schaal, 2020. "Optimal Transport Networks in Spatial Equilibrium," Econometrica, Econometric Society, vol. 88(4), pages 1411-1452, July.
    2. Alvarez-Cuadrado, Francisco & Long, Ngo & Poschke, Markus, 2017. "Capital-labor substitution, structural change and growth," Theoretical Economics, Econometric Society, vol. 12(3), September.
    3. Ngo Long & Vincent Martinet, 2018. "Combining rights and welfarism: a new approach to intertemporal evaluation of social alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 35-64, January.
    4. Crettez, Bertrand & Hayek, Naila & Zaccour, Georges, 2023. "When is frugality optimal?," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 65-75.
    5. Fritz, Oliver M. & Sonis, Michael & Hewings, Geoffrey J. D., 1998. "A Miyazawa analysis of interactions between polluting and non-polluting sectors," Structural Change and Economic Dynamics, Elsevier, vol. 9(3), pages 289-305, September.
    6. Cheng, John Q & Wellman, Michael P, 1998. "The WALRAS Algorithm: A Convergent Distributed Implementation of General Equilibrium Outcomes," Computational Economics, Springer;Society for Computational Economics, vol. 12(1), pages 1-24, August.
    7. Giorgio Giorgi, 2022. "Nonsingular M-matrices: a Tour in the Various Characterizations and in Some Related Classes," DEM Working Papers Series 206, University of Pavia, Department of Economics and Management.
    8. Georg Meran & Christian Hirschhausen, 2009. "A modified yardstick competition mechanism," Journal of Regulatory Economics, Springer, vol. 35(3), pages 223-245, June.
    9. Engwerda, J.C., 2007. "Necessary and Sufficient Conditions for Solving Cooperative Differential Games," Discussion Paper 2007-42, Tilburg University, Center for Economic Research.
    10. Fleurbaey, Marc & Gary-Bobo, Robert J. & Maguain, Denis, 2002. "Education, distributive justice, and adverse selection," Journal of Public Economics, Elsevier, vol. 84(1), pages 113-150, April.
    11. Vicent Alcantara, 2015. "Economic growth and productive structure in an input/output model: An alternative coefficient sensitivity analysis (english version of working paper 11.08)," Working Papers wpdea1504, Department of Applied Economics at Universitat Autonoma of Barcelona.
    12. Buhr, Brian L. & Kim, Hanho, 1997. "Dynamic adjustment in the US beef market with imports," Agricultural Economics, Blackwell, vol. 17(1), pages 21-34, October.
    13. Kort, P.M., 1993. "Pollution Control and the Dynamics of Firm : The Effects of Market Based Instruments on Optimal Firm Investments," Other publications TiSEM 7f93f736-2e2e-41e2-a3b5-c, Tilburg University, School of Economics and Management.
    14. Kitamura, Yoshihiro, 2010. "Testing for intraday interdependence and volatility spillover among the euro, the pound and the Swiss franc markets," Research in International Business and Finance, Elsevier, vol. 24(2), pages 158-171, June.
    15. Gunter M. Schutz & Fernando Pigeard de Almeida Prado & Rosemary J. Harris & Vladimir Belitsky, 2007. "Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents," Papers 0801.0003, arXiv.org, revised Jun 2009.
    16. Julia Müller & Thorsten Upmann & Joachim Prinz, 2013. "Individual Team Productivity - A Conceptual Approach," Tinbergen Institute Discussion Papers 13-183/I, Tinbergen Institute.
    17. Paolo Bertoletti & Giorgio Rampa, 2013. "On inferior inputs and marginal returns," Journal of Economics, Springer, vol. 109(3), pages 303-313, July.
    18. L. Grosset & B. Viscolani, 2006. "Reciprocal Optimal Control Problems and the Associated Pareto Frontier," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 113-123, July.
    19. Engwerda, J.C., 2007. "Multicriteria Dynamic Optimization Problems and Cooperative Dynamic Games," Other publications TiSEM c7941fef-278b-42ca-a6b8-2, Tilburg University, School of Economics and Management.
    20. Beteto, Danilo Lopomo, 2012. "Government Intervention and Financial Fragility," Risk and Sustainable Management Group Working Papers 156477, University of Queensland, School of Economics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:116:y:2006:i:11:p:1530-1562. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.