Skip to main content
Log in

Portfolio management without probabilities or statistics

  • Research Article
  • Published:
Annals of Finance Aims and scope Submit manuscript

Abstract

Considered here is on-line portfolio management aimed at maximizing the long-run growth of financial wealth. The portfolio is repeatedly rebalanced in response to observed returns on diverse assets. Suppose statistical information and related methods are not available—or deemed too difficult. On that assumption this paper explores how an adaptive procedure, which totally dispenses with statistics and associated competence, nonetheless may solve the problem over time.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Algoet P.H., Cover T.M.: Asymptotic optimality and asymptotic equipartition properties of log-optimum investment. Ann Probab 16(2), 876–898 (1988)

    Article  Google Scholar 

  • Allais M.: Le comportement de l’homme devant le risque: Critique des postulats et axiomes de l’école américaine. Econometrica 21, 503 (1953)

    Article  Google Scholar 

  • Amir R., Evstigneev I.V., Hens T., Schenk-Hoppé K.R.: Market selection and survival of investment strategies. J Math Econ 41, 105–122 (2005)

    Article  Google Scholar 

  • Benaim M.: A dynamical system approach to stochastic approximation. SIAM J Control Optim 34, 437–472 (1996)

    Article  Google Scholar 

  • Benveniste A., Métivier M., Priouret P.: Adaptive Algorithms and Stochastic Approximations. Springer, Berlin (1990)

    Google Scholar 

  • Blume L., Easley D.: Evolution and market behavior. J Econ Theory 58, 9–40 (1992)

    Article  Google Scholar 

  • Chung K.L.: A Course in Probability Theory, 2nd edn. Academic Press, San Diego (1974)

    Google Scholar 

  • Cover T.M.: An algorithm for maximizing expected log investment return. IEEE Trans Inf Theory 30(2), 369–373 (1984)

    Article  Google Scholar 

  • Cover T.M., Thomas J.A.: Elements of Information Theory. Wiley, New York (1991)

    Book  Google Scholar 

  • Dempster M.A.H., Evstigneev I.V., Schenk-Hoppé K.R.: Exponential growth of fixed-mix strategies in stationary asset markets. Financ Stochast 7, 263–276 (2003)

    Article  Google Scholar 

  • Epstein L.G., Zin S.E.: Substitution, risk aversion, and the temporal behavior of consumption and asset returns: a theoretical framework. Econometrica 57, 937–969 (1989)

    Article  Google Scholar 

  • Ermoliev Y.: Methods of Stochastic Programming (in Russian). Nauka, Moscow (1976)

    Google Scholar 

  • Evstigneev I.V., Schenk-Hoppé K.R.: From rags to riches: on constant proportions investment strategies. Int J Theor Appl Financ 5(6), 563–573 (2002)

    Article  Google Scholar 

  • Evstigneev I.V., Hens T., Schenk-Hoppé K.R.: Market selection of financial trading strategies: global stability. Math Financ 12, 329–339 (2002)

    Article  Google Scholar 

  • Gaivoronski A.A., Stella F.: On-line portfolio selection using stochastic programming. J Econ Dyn Control 27, 1013–1043 (2003)

    Article  Google Scholar 

  • Gaivoronski A.A., Stella F.: Stochastic nonstationary optimization for finding universal portfolios. Ann Oper Res 100, 165–188 (2000)

    Article  Google Scholar 

  • Grinblatt M., Titman S., Wermers R.: Momentum investment strategies, portfolio performance, and herding: a study of mutual fund behavior. Am Econ Rev 85(5), 1088–1105 (1995)

    Google Scholar 

  • Hakansson N.H.: On optimal myopic portfolio policies, with and without serial correlation yields. J Bus 44(3), 324–334 (1971)

    Article  Google Scholar 

  • Hens T., Schenk-Hoppé K.R. (2005a) Special Issue on Evolutionary Finance. J Math Econ 41, 1–5

    Article  Google Scholar 

  • Hens T., Schenk-Hoppé K.R. (2005b) Evolutionary stability of portfolio rules in incomplete markets. J Math Econ 41, 43–66

    Article  Google Scholar 

  • Hofbauer J., Sigmund K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  • Iyengar G.N., Cover T.M.: Growth optimal investment in horse race markets with costs. IEEE Trans Inf Theory 46(7), 2675–2683 (2000)

    Article  Google Scholar 

  • Kelly J.L.: A new interpretation of the information rate. Bell Syst Tech J 35, 917–926 (1956)

    Google Scholar 

  • Levy H.: Experimental economics and the theory of finance. In: Lee, C.-F., Lee, A.C. (eds) Encyclopedia of Finance., pp. 520–540. Springer, Berlin (2006)

    Chapter  Google Scholar 

  • Long J.B.: The numeraire portfolio. J Financial Econ 26, 29–69 (1990)

    Article  Google Scholar 

  • Luenberger D.G.: Investment Science. Oxford University Press, Oxford (1998)

    Google Scholar 

  • Michelot C.: A finite algorithm for finding the projection of a point onto the canonical simplex of R n. J Optim Theory Appl 50(1), 195–200 (1986)

    Article  Google Scholar 

  • Mossin J.: Optimal multiperiod portfolio policies. J Bus 41, 215–229 (1968)

    Article  Google Scholar 

  • Robbins H., Siegmund D.: A convergence theorem for non-negative almost surmartingales and some applications. In: Rustagi, J. (eds) Optimization Methods in Statistics., pp. 235–257. Academic Press, New York (1971)

    Google Scholar 

  • Rudin W.: Principles of Mathematical Analysis. McGraw-Hill, New York (1964)

    Google Scholar 

  • Sutton R.S., Barto A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge (1998)

    Google Scholar 

  • Vega-Redondo F.: Economics and the Theory of Games. MIT Press, Cambridge (2003)

    Google Scholar 

  • Weibull J.: Evolutionary Game Theory. MIT Press, Cambridge (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sjur Didrik Flåm.

Additional information

Support from Finansmarkedsfondet, University of Lund, STINT, and University of Zürich is gratefully acknowledged. Thanks are due a referee for most helpful remarks.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Flåm, S.D. Portfolio management without probabilities or statistics. Ann Finance 6, 357–368 (2010). https://doi.org/10.1007/s10436-008-0106-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10436-008-0106-6

Keywords

JEL Classification

Navigation