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A Stochastic Differential Equation for Modeling the “Classical” Probability Distributions

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  • Hertzler, Greg

Abstract

Stochastic differential equations are a flexible way to model continuous probability distributions. The most popular differential equations are for non-stationary Lognormal, non-stationary Normal and stationary Ornstein-Uhlenbeck distributions. The probability densities are known for these distributions and the assumptions behind the differential equations are well understood. Unfortunately, the assumptions do not fit most situations. In economics and finance, prices and quantities are usually stationary and positive. The Lognormal and Normal distributions are nonstationary and the Normal and Ornstein-Uhlenbeck distributions allow negative prices and quantities. This study derives a stochastic differential equation that includes most of the classical probability distributions as special cases and greatly expands the number distributions that can be used in models of stochastic dynamic systems.

Suggested Citation

  • Hertzler, Greg, 2003. "A Stochastic Differential Equation for Modeling the “Classical” Probability Distributions," 2003 Conference (47th), February 12-14, 2003, Fremantle, Australia 57891, Australian Agricultural and Resource Economics Society.
  • Handle: RePEc:ags:aare03:57891
    DOI: 10.22004/ag.econ.57891
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    Cited by:

    1. Zheng, Wenyuan & Li, Bingqing & Huang, Zhiyong & Chen, Lu, 2022. "Why Was There More Household Stock Market Participation During the COVID-19 Pandemic?," Finance Research Letters, Elsevier, vol. 46(PB).
    2. Nelson Christopher Dzupire & Philip Ngare & Leo Odongo, 2019. "Pricing Basket Weather Derivatives on Rainfall and Temperature Processes," IJFS, MDPI, vol. 7(3), pages 1-14, June.

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    Keywords

    Research Methods/ Statistical Methods;

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