Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Cover of the book

2021 | OriginalPaper | Chapter

1. Introduction

Authors : Tomas Björk, Mariana Khapko, Agatha Murgoci

Published in: Time-Inconsistent Control Theory with Finance Applications

Publisher: Springer International Publishing

Log in

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

search-config
loading …

Abstract

In this chapter we introduce the concept of time inconsistency in dynamic choice problems. We start by reviewing the key ideas of dynamic programming and listing the main reasons for the time consistency in a given problem. We then present a number of seemingly simple examples from financial economics in which time consistency fails to hold. To tackle these (and similar problems), we outline the different approaches developed in the literature for handling time inconsistency in a dynamic stochastic control setting. In this book, we take the game-theoretic approach and look for subgame-perfect equilibrium strategies. Additionally, we emphasize that, similar to control problems, a stopping problem can be time inconsistent if it does not admit a Bellman optimality principle.

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!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

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!

inform now
next chapter Dynamic Programming Theory
Literature
Bajeux-Besnainou, I., & Portait, R. (1998). Dynamic asset allocation in a mean-variance framework. Management Science, 44(11), 79–95.CrossRef
Barro, R. (1999). Ramsey meets Laibson in the neoclassical growth model. The Quarterly Journal of Economics, 114, 1125–1152.CrossRef
Basak, S., & Chabakauri, G. (2010). Dynamic mean-variance asset allocation. Review of Financial Studies, 23, 2970–3016.CrossRef
Björk, T., & Murgoci, A. (2014). A theory of Markovian time-inconsistent stochastic control in discrete time. Finance and Stochastics, 18, 545–592.MathSciNetCrossRef
Björk, T., Murgoci, A., & Khapko, M. (2017). On time-inconsistent stochastic control in continuous time. Finance and Stochastics, 21, 331–360.MathSciNetCrossRef
Björk, T., Murgoci, A., & Zhou, X. Y. (2014). Mean-variance portfolio optimization with state-dependent risk aversion. Mathematical Finance, 24, 1–24.MathSciNetCrossRef
Czichowsky, C. (2013). Time-consistent mean-variance portfolio selection in discrete and continuous time. Finance and Stochastics, 17, 227–271.MathSciNetCrossRef
Dai, M., Jin, H., Kou, S., & Xu, Y. (2021). A dynamic mean-variance analysis for log returns. Management Science, 67(2), 1093–1108.CrossRef
Djehiche, B., & Huang, M. (2016). A characterization of sub-game perfect equilibria for SDEs of mean-field type. Dynamic Games and Applications, 6, 55–81.MathSciNetCrossRef
Dong, Y., & Sircar, R. (2014). Time-inconsistent portfolio investment problems. In D. Crisan, B. Hambly, & T. Zariphopoulou (Eds.), Stochastic analysis and applications (pp. 239–281). Springer.
Ekeland, I., & Lazrak, A. (2010). The golden rule when preferences are time inconsistent. Mathematics and Financial Economics, 4, 29–55.MathSciNetCrossRef
Ekeland, I., Mbodji, O., & Pirvu, T. (2010). Time-consistent portfolio management. SIAM Journal on Financial Mathematics, 3, 1–32.MathSciNetCrossRef
Ekeland, I., & Pirvu, T. (2008). Investment and consumption without commitment. Mathematics and Financial Economics, 2(1), 57–86.MathSciNetCrossRef
Goldman, S. (1980). Consistent plans. Review of Economic Studies, 47, 533–537.CrossRef
Harris, C., & Laibson, D. (2013). Instantaneous gratification. The Quarterly Journal of Economics, 128(1), 205–248.CrossRef
Hu, Y., Jin, H., & Zhou, X. (2012). Time-inconsistent stochastic linear-quadratic control. SIAM Journal on Control and Optimization, 50(3), 1548–1572.MathSciNetCrossRef
Kronborg, M. T., & Steffensen, M. (2015). Inconsistent investment and consumption problems. Applied Mathematics & Optimization, 71(3), 473–515.MathSciNetCrossRef
Krusell, P., & Smith, A. (2003). Consumption and savings decisions with quasi-geometric discounting. Econometrica, 71, 366–375.CrossRef
Landriault, D., Li, B., Li, D., & Young, V. R. (2018). Equilibrium strategies for the mean-variance investment problem over a random horizon. SIAM Journal on Financial Mathematics, 9(3), 1046–1073.MathSciNetCrossRef
Li, D., & Ng, W. (2000). Optimal dynamic portfolio selection: Multi-period mean-variance formulation. Mathematical Finance, 10, 387–406.MathSciNetCrossRef
Li, D., Rong, X., & Zhao, H. (2015b). Time-consistent reinsurance–investment strategy for a mean–variance insurer under stochastic interest rate model and inflation risk. Insurance Mathematics and Economics, 64, 28–44.MathSciNetCrossRef
Lioui, A. (2013). Time consistent vs. time inconsistent dynamic asset allocation: Some utility cost calculations for mean variance preferences. Journal of Economic Dynamics and Control, 37(5), 1066–1096.MathSciNetCrossRef
Marín-Solano, J., & Navas, J. (2010). Consumption and portfolio rules for time-inconsistent investors. European Journal of Operational Research, 201(3), 860–872.MathSciNetCrossRef
Pedersen, J., & Peskir, G. (2016). Optimal mean-variance selling strategies. Mathematics and Financial Economics, 10, 203–220.MathSciNetCrossRef
Pedersen, J., & Peskir, G. (2017). Optimal mean-variance portfolio selection. Mathematics and Financial Economics, 11, 1–24.MathSciNetCrossRef
Peleg, B., & Yaari, M. E. (1973). On the existence of a consistent course of action when tastes are changing. Review of Economic Studies, 40, 391–401.CrossRef
Pirvu, T., & Zhang, H. (2014). Investment-consumption with regime-switching discount rates. Mathematical Social Sciences, 71, 142–150.MathSciNetCrossRef
Pollak, R. (1968). Consistent planning. Review of Economic Studies, 35, 185–199.CrossRef
Richardson, H. R. (1989). A minimum variance result in continuous trading portfolio optimization. Management Science, 35(9), 1045–1055.MathSciNetCrossRef
Strotz, R. (1955). Myopia and inconsistency in dynamic utility maximization. Review of Economic Studies, 23, 165–180.CrossRef
van Staden, P. M., Dang, D.-M., & Forsyth, P. A. (2019). Mean-quadratic variation portfolio optimization: A desirable alternative to time-consistent mean-variance optimization? SIAM Journal on Financial Mathematics, 10(3), 815–856.MathSciNetCrossRef
van Staden, P. M., Dang, D.-M., & Forsyth, P. A. (2021). The surprising robustness of dynamic mean-variance portfolio optimization to model misspecification errors. European Journal of Operational Research, 289(2), 774–792.MathSciNetCrossRef
Vieille, N., & Weibull, J. (2009). Multiple solutions under quasi-exponential discounting. Economic Theory, 39, 513–526.MathSciNetCrossRef
Vigna, E. (2020). On time consistency for mean-variance portfolio selection. International Journal of Theoretical and Applied Finance, 23(06), 1–22.MathSciNetCrossRef
Wang, J., & Forsyth, P. A. (2012). Comparison of mean variance like strategies for optimal asset allocation problems. International Journal of Theoretical and Applied Finance, 15(02), Article 1250014.
Zhou, X. Y., & Li, D. (2000). Continuous-time mean-variance portfolio selection: A stochastic LQ framework. Applied Mathematics and Optimization, 42, 19–33.MathSciNetCrossRef
Zhou, Z., Ren, T., Xiao, H., & Liu, W. (2019). Time-consistent investment and reinsurance strategies for insurers under multi-period mean-variance formulation with generalized correlated returns. Journal of Management Science and Engineering, 4(2), 142–157.CrossRef
Metadata
Title
Introduction
Authors
Tomas Björk
Mariana Khapko
Agatha Murgoci
Copyright Year
2021
Book
Time-Inconsistent Control Theory with Finance Applications

Print ISBN: 978-3-030-81842-5

Electronic ISBN: 978-3-030-81843-2

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-81843-2_1

Premium Partner

    Image Credits