Skip to main content
Springer Nature Link
Log in

Behavioral Dynamic Portfolio Selection via Epsilon-Contaminations

  • Conference paper
  • First Online:
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2024)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 1176))

  • 6 Accesses

Abstract

We consider a dynamic portfolio selection problem in a finite horizon binomial market model, composed of a non-dividend-paying risky stock and a risk-free bond. We assume that the investor’s behavior distinguishes between gains and losses, as in the classical cumulative prospect theory (CPT). This is achieved by considering preferences that are represented by a CPT-like functional, depending on an S-shaped utility function. At the same time, we model investor’s beliefs on gains and losses through two different epsilon-contaminations of the “real-world” probability measure. We formulate the portfolio selection problem in terms of the final wealth and reduce it to an iterative search problem over the set of optimal solutions of a family of non-linear optimization problems.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Allais, M.: Le comportement de l’homme rationnel devant le risque: Critique des postulats et axiomes de l’ecole americaine. Econometrica 21(4), 503–546 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  2. Antonini, P., Petturiti, D., Vantaggi, B.: Dynamic portfolio selection under ambiguity in the \(\epsilon \)-contaminated binomial model. In: Lesot, M.J., et al. (eds.) Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 210–223. Springer (2020)

    Google Scholar 

  3. Bi, J., Jin, H., Meng, Q.: Behavioral mean-variance portfolio selection. Eur. J. Oper. Res. 271(2), 644–663 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  4. Černý, A.: Mathematical Techniques in Finance: Tools for Incomplete Markets. 2nd edn., Princeton University Press (2009)

    Google Scholar 

  5. Couenne (2024). https://www.coin-or.org/Couenne/

  6. Cox, J., Ross, S., Rubinstein, M.: Option pricing: a simplified approach. J. Financ. Econ. 7(3), 229–263 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  7. Duffie, D.: Dynamic Asset Pricing Theory. Priceton University Press, 3rd edn. (2001)

    Google Scholar 

  8. Ellsberg, D.: Risk, ambiguity, and the savage axioms. Q. J. Econ. 75(4), 643–669 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  9. Harris, R., Mazibas, M.: Portfolio optimization with behavioural preferences and investor memory. Eur. J. Oper. Res. 296(1), 368–387 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  10. Huber, P.J.: Robust Statistics. Wiley, New York (1981)

    Book  MATH  Google Scholar 

  11. Jin, H., Yu Zhou, X.: Behavioral portfolio selection in continuous time. Math. Financ. 18(3), 385–426 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47(2), 263–291 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  13. Montes, I., Miranda, E., Destercke, S.: Unifying neighbourhood and distortion models: part I - new results on old models. Int. J. Gen Syst 49(6), 602–635 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  14. Munk, C.: Financial Asset Pricing Theory. Oxford University Press (2013)

    Google Scholar 

  15. Petturiti, D., Vantaggi, B.: The impact of ambiguity on dynamic portfolio selection in the epsilon-contaminated binomial market model. Eur. J. Oper. Res. 314(3), 1029–1039 (2024)

    Article  MathSciNet  MATH  Google Scholar 

  16. Pyomo (2024). http://www.pyomo.org/

  17. Quiggin, J.: A theory of anticipated utility. J. Econ. Behav. Organ. 3(4), 323–343 (1982)

    Article  MATH  Google Scholar 

  18. Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertain. 5(4), 297–323 (1992)

    Article  MATH  Google Scholar 

  19. von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Priceton University Press (1944)

    Google Scholar 

  20. Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)

    Book  MATH  Google Scholar 

  21. Yaari, M.: The dual theory of choice under risk. Econometrica 55(1), 95–115 (1987)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

We acknowledge the support of the PRIN 2022 project “Models for dynamic reasoning under partial knowledge to make interpretable decisions” (Project number: 2022AP3B3B, CUP Master: J53D23004340006, CUP: B53D23009860006) funded by the European Union – Next Generation EU. The first author has been supported by the Sapienza University of Rome research project “Frictions meet incompleteness: no-arbitrage solutions for derivative pricing and investment opportunities” (Grant: RM1221816C3DDAC2).

Author information

Authors and Affiliations

  1. Department MEMOTEF, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  2. Department Economics, University of Perugia, Perugia, Italy

    Andrea Cinfrignini & Davide Petturiti

Authors
  1. Andrea Cinfrignini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Davide Petturiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Barbara Vantaggi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrea Cinfrignini .

Editor information

Editors and Affiliations

  1. LIP6, BC169, Sorbonne Université, PARIS, France

    Marie-Jeanne Lesot

  2. IDMEC,Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    Susana Vieira

  3. Electrical and Computer Engineering, University of Alberta, Edmonton, Canada

    Marek Z. Reformat

  4. INESC-ID,Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    João Paulo Carvalho

  5. INESC-ID, Av. das Forças Armadas, 1649-026, ISCTE - University Institute of Lisbon, Lisboa, Portugal

    Fernando Batista

  6. LIP6, BC169, Place Jussieu 4, 75005, Sorbonne University, Paris, France

    Bernadette Bouchon-Meunier

  7. Machine Intelligence Institute, Iona Collage, NEW ROCHELLE, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2025 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cinfrignini, A., Petturiti, D., Vantaggi, B. (2025). Behavioral Dynamic Portfolio Selection via Epsilon-Contaminations. In: Lesot, MJ., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2024. Lecture Notes in Networks and Systems, vol 1176. Springer, Cham. https://doi.org/10.1007/978-3-031-73997-2_16

Download citation

Publish with us

Policies and ethics