Skip to main content
Top

2019 | OriginalPaper | Chapter

7. Optimal Control

Authors : Ernst Eberlein, Jan Kallsen

Published in: Mathematical Finance

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Dynamic stochastic optimisation problems play an important role in Mathematical Finance and other applications. In this chapter we provide basic tools for their mathematical treatment in continuous time.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
14.
go back to reference B. Bassan, C. Ceci, Regularity of the value function and viscosity solutions in optimal stopping problems for general Markov processes. Stochastics Stochastics Rep. 74(3–4), 633–649 (2002)MathSciNetCrossRef B. Bassan, C. Ceci, Regularity of the value function and viscosity solutions in optimal stopping problems for general Markov processes. Stochastics Stochastics Rep. 74(3–4), 633–649 (2002)MathSciNetCrossRef
28.
76.
go back to reference C. Dellacherie, P.-A. Meyer, Probabilities and Potential B: Theory of Martingales (North-Holland, Amsterdam, 1982)MATH C. Dellacherie, P.-A. Meyer, Probabilities and Potential B: Theory of Martingales (North-Holland, Amsterdam, 1982)MATH
96.
go back to reference N. El Karoui, Les aspects probabilistes du contrôle stochastique, in Ninth Saint Flour Probability Summer School—1979 (Saint Flour, 1979), volume 876 of Lecture Notes in Math. (Springer, Berlin, 1981), pp. 73–238 N. El Karoui, Les aspects probabilistes du contrôle stochastique, in Ninth Saint Flour Probability Summer School—1979 (Saint Flour, 1979), volume 876 of Lecture Notes in Math. (Springer, Berlin, 1981), pp. 73–238
112.
go back to reference W. Fleming, M. Soner, Controlled Markov Processes and Viscosity Solutions, 2nd edn. (Springer, New York, 2006)MATH W. Fleming, M. Soner, Controlled Markov Processes and Viscosity Solutions, 2nd edn. (Springer, New York, 2006)MATH
115.
go back to reference H. Föllmer, P. Protter, Local martingales and filtration shrinkage. ESAIM Probab. Stat. 15(In honor of Marc Yor, suppl.), S25–S38 (2011) H. Föllmer, P. Protter, Local martingales and filtration shrinkage. ESAIM Probab. Stat. 15(In honor of Marc Yor, suppl.), S25–S38 (2011)
126.
go back to reference T. Goll, J. Kallsen, A complete explicit solution to the log-optimal portfolio problem. Ann. Appl. Probab. 13(2), 774–799 (2003)MathSciNetCrossRef T. Goll, J. Kallsen, A complete explicit solution to the log-optimal portfolio problem. Ann. Appl. Probab. 13(2), 774–799 (2003)MathSciNetCrossRef
135.
154.
go back to reference J. Jacod, A. Shiryaev, Limit Theorems for Stochastic Processes, 2nd edn. (Springer, Berlin, 2003)CrossRef J. Jacod, A. Shiryaev, Limit Theorems for Stochastic Processes, 2nd edn. (Springer, Berlin, 2003)CrossRef
206.
go back to reference M. Lenga, Representable Options. PhD thesis, Kiel University, 2017 M. Lenga, Representable Options. PhD thesis, Kiel University, 2017
217.
go back to reference R. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case. Rev. Econ. Stat. 51(3), 247–257 (1969)CrossRef R. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case. Rev. Econ. Stat. 51(3), 247–257 (1969)CrossRef
218.
go back to reference R. Merton, Optimum consumption and portfolio rules in a continuous-time model. J. Econom. Theory 3(4), 373–413 (1971)MathSciNetCrossRef R. Merton, Optimum consumption and portfolio rules in a continuous-time model. J. Econom. Theory 3(4), 373–413 (1971)MathSciNetCrossRef
226.
go back to reference B. Øksendal, Stochastic Differential Equations, 6th edn. (Springer, Berlin, 2003)CrossRef B. Øksendal, Stochastic Differential Equations, 6th edn. (Springer, Berlin, 2003)CrossRef
227.
go back to reference B. Øksendal, A. Sulem, Applied Stochastic Control of Jump Diffusions, 2nd edn. (Springer, Berlin, 2007)CrossRef B. Øksendal, A. Sulem, Applied Stochastic Control of Jump Diffusions, 2nd edn. (Springer, Berlin, 2007)CrossRef
232.
go back to reference G. Peskir, A. Shiryaev, Optimal Stopping and Free-Boundary Problems (Birkhäuser, Basel, 2006) G. Peskir, A. Shiryaev, Optimal Stopping and Free-Boundary Problems (Birkhäuser, Basel, 2006)
234.
go back to reference H. Pham, Continuous-Time Stochastic Control and Optimization with Financial Applications (Springer, Berlin, 2009)CrossRef H. Pham, Continuous-Time Stochastic Control and Optimization with Financial Applications (Springer, Berlin, 2009)CrossRef
260.
go back to reference W. Schachermayer, M. Sîrbu, E. Taflin, In which financial markets do mutual fund theorems hold true? Finance Stochast. 13(1), 49–77 (2009)MathSciNetCrossRef W. Schachermayer, M. Sîrbu, E. Taflin, In which financial markets do mutual fund theorems hold true? Finance Stochast. 13(1), 49–77 (2009)MathSciNetCrossRef
270.
go back to reference M. Schweizer, A guided tour through quadratic hedging approaches. Option Pricing, Interest Rates and Risk Management (Cambridge Univ. Press, Cambridge, 2001), pp. 538–574 M. Schweizer, A guided tour through quadratic hedging approaches. Option Pricing, Interest Rates and Risk Management (Cambridge Univ. Press, Cambridge, 2001), pp. 538–574
271.
go back to reference A. Seierstad, Stochastic Control in Discrete and Continuous Time (Springer, New York, 2009)CrossRef A. Seierstad, Stochastic Control in Discrete and Continuous Time (Springer, New York, 2009)CrossRef
287.
go back to reference N. Touzi, Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE (Springer, New York, 2013)CrossRef N. Touzi, Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE (Springer, New York, 2013)CrossRef
295.
go back to reference J. Yong, X. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations (Springer, New York, 1999)CrossRef J. Yong, X. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations (Springer, New York, 1999)CrossRef
Metadata
Title
Optimal Control
Authors
Ernst Eberlein
Jan Kallsen
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-030-26106-1_7