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Discretisation of Stochastic Control Problems for Continuous Time Dynamics with Delay

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Author Info
Markus Fischer
Markus Reiss
Abstract

As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretizing time and space. A new feature in this context is to allow for delay in the dynamics. The existence of an optimal strategy with respect to the cost functional can be guaranteed in the class of relaxed controls. Weak convergence of the approximating extended Markov chains to the original process together with convergence of the associated optimal strategies is established.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2005-038.pdf
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File Function: Revised version, 2005
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Publisher Info
Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2005-038.

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Length: 25 pages
Date of creation: Aug 2005
Date of revision: Dec 2005
Handle: RePEc:hum:wpaper:sfb649dp2005-038

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Keywords: Markov Markov chain time dynamics stochastic control problem

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C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques

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  1. Szymon Borak & Kai Detlefsen & Wolfgang Härdle, 2005. "FFT Based Option Pricing," SFB 649 Discussion Papers SFB649DP2005-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  2. Ralf Brüggemann & Carsten Trenkler, 2005. "Are Eastern European Countries Catching Up? Time Series Evidence for Czech Republic, Hungary, and Poland," SFB 649 Discussion Papers SFB649DP2005-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
    Other versions:
  3. Eun-Kyung Lee & Dianne Cook & Sigbert Klinke & Thomas Lumley, 2005. "Projection Pursuit for Exploratory Supervised Classification," SFB 649 Discussion Papers SFB649DP2005-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  4. Silke Anger, 2005. "Working Time as an Investment? : The Effects of Unpaid Overtime on Wages, Promotions, and Layoffs," Discussion Papers of DIW Berlin 535, DIW Berlin, German Institute for Economic Research. [Downloadable!]
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  5. Sigbert Klinke & Uwe Ziegenhagen & Yuval Guri, 2005. "Yxilon – a Modular Open-Source Statistical Programming Language," SFB 649 Discussion Papers SFB649DP2005-018, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  6. Enzo Giacomini & Wolfgang Härdle, 2005. "Value-at-Risk Calculations with Time Varying Copulae," SFB 649 Discussion Papers SFB649DP2005-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  7. Oliver Blaskowitz & Helmut Herwartz & Gonzalo de Cadenas Santiago, 2005. "Modeling the FIBOR/EURIBOR Swap Term Structure: An Empirical Approach," SFB 649 Discussion Papers SFB649DP2005-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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  8. Dirk Krueger & Harald Uhlig, 2005. "Competitive Risk Sharing Contracts with One-Sided Commitment," CFS Working Paper Series 2005/07, Center for Financial Studies. [Downloadable!]
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  9. Szymon Borak & Matthias Fengler & Wolfgang Härdle, 2005. "DSFM fitting of Implied Volatility Surfaces," SFB 649 Discussion Papers SFB649DP2005-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  10. Alexander Schied & Ching-Tang Wu, 2005. "Duality theory for optimal investments under model uncertainty," SFB 649 Discussion Papers SFB649DP2005-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Sep 2005. [Downloadable!]
  11. Yasemin Boztug & Lutz Hildebrandt, 2005. "A Market Basket Analysis Conducted with a Multivariate Logit Model," SFB 649 Discussion Papers SFB649DP2005-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  12. Ronald Bachmann, 2005. "Skill mismatch in equilibrium unemployment," SFB 649 Discussion Papers SFB649DP2005-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, revised Aug 2005. [Downloadable!]
  13. Astrid Matthey, 2005. "Getting Used to Risks: Reference Dependence and Risk Inclusion," SFB 649 Discussion Papers SFB649DP2005-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  14. Schabert, Andreas & Stoltenberg, Christian, 2005. "Money Demand and Macroeconomic Stability Revisited," CEPR Discussion Papers 4974, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  15. Almuth Scholl & Harald Uhlig, 2005. "New Evidence on the Puzzles. Results from Agnostic Identification on Monetary Policy and Exchange Rates," SFB 649 Discussion Papers SFB649DP2005-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  16. Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
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