A hyperbolic model of optimal cash balances

John van der Burg, Xiaojing Song, Mark Tippett

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2 Citations (Scopus)
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We develop a hyperbolic cash management model based on the Pearson Type IV probability density which minimises extreme variations in firm cash balances. Since the moments for the Type IV probability density are in general undefined and maximum likelihood estimation is compromised by the non-algebraic nature of the Type IV normalising constant, parameter estimation is implemented using the minimum method. Empirical analysis shows that the Type IV density is highly compatible with the quarterly cash flow data of a randomly selected sample of 100 large U.S. corporations. In contrast, around 60% of the 100 corporations return Jarque–Bera test statistics which are incompatible with the Gaussian probability density.
Original languageEnglish
Pages (from-to)101-115
Number of pages15
JournalThe European Journal of Finance
Issue number2
Early online date11 Jun 2018
Publication statusPublished - 22 Jan 2019


  • Cash balance
  • hyperbolic
  • Hamilton–Jacobi–Bellman equation
  • Pearson Type IV probability density

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