Skip to main content

Part of the book series: Springer Finance ((FINANCE))

  • 1226 Accesses

Abstract

We now go on to study a class of time-inconsistent control problems. Before proceeding to the formal theory, we first recall a part of our discussion on the Bellman optimality principle from the Introduction. We then detail the game-theoretic formulation, whereby we view the problem as a non-cooperative game with one player at each point in time representing different incarnations of decision maker’s preferences. The main result of this chapter is the extension of the standard Bellman equation, in the form of a system of nonlinear equations, for the determination of the equilibrium strategy and the equilibrium value function. We arrive at the extended Bellman system by first studying a couple of simpler problems to highlight the main ideas and then by bringing things together for the general case.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Strotz, R. (1955). Myopia and inconsistency in dynamic utility maximization. Review of Economic Studies, 23, 165–180.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Björk, T., Khapko, M., Murgoci, A. (2021). Time-Inconsistent Control Theory. In: Time-Inconsistent Control Theory with Finance Applications. Springer Finance. Springer, Cham. https://doi.org/10.1007/978-3-030-81843-2_5

Download citation

Publish with us

Policies and ethics