A unique optimal stock–bond mix for all long-run investors

Moshe Levy*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Life expectancy has increased significantly over the last century, implying a substantial lengthening of the investment horizon. We consider the portfolio choice problem of long-run investors in a setting with three assets: stocks, risky bonds, and a risk-free asset. We show that in the benchmark continuous-time framework there is a unique stock–bond mix that is optimal for all investors with non-decreasing preferences, including Prospect Theory investors, and investors with various aspiration levels. In discrete time, there is a set of efficient stock–bond mixtures. As the investment horizon increases, this set shrinks quickly and converges to the unique continuous-time optimal solution.

Original languageAmerican English
JournalAnnals of Operations Research
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • First-degree Stochastic Dominance (FSD)
  • Investment horizon
  • Lognormal distribution
  • Prospect theory
  • Stocks versus bonds


Dive into the research topics of 'A unique optimal stock–bond mix for all long-run investors'. Together they form a unique fingerprint.

Cite this