Dynamical optimization theory of a diversified portfolio

Matteo Marsili, Sergei Maslov, Yi Cheng Zhang

Research output: Contribution to journalArticlepeer-review


We propose and study a simple model of dynamical redistribution of capital in a diversified portfolio. We consider a hypothetical situation of a portfolio composed of N uncorrelated stocks. Each stock price follows a multiplicative random walk with identical drift and dispersion. The rules of our model naturally give rise to power law tails in the distribution of capital fractions invested in different stocks. The exponent of this scale free distribution is calculated in both discrete and continuous time formalism. It is demonstrated that the dynamical redistribution strategy results in a larger typical growth rate of the capital than a static "buy-and-hold" strategy. In the large N limit the typical growth rate is shown to asymptotically approach that of the expectation value of the stock price. The finite dimensional variant of the model is shown to describe the partition function of directed polymers in random media.

Original languageEnglish (US)
Pages (from-to)403-418
Number of pages16
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-4
StatePublished - May 1 1998
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


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