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The Conditional Probability Density Function for a Reflected Brownian Motion

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  • Dirk Veestraeten

Abstract

Models in economics and other fields often require a restricted Brownian motion because frequently implicit or explicit barriers restrict the domain. This paper contributes to the literature on reflected Brownian motion by deriving its conditional density function as a closed-form expression that consists of infinite sums of Gaussian densities. This solution is compared with an alternative, trigonometric expression derived earlier. Numerical analyses reveal that convergence properties of the expression derived in this paper are superior to those of the alternative representation for most practically relevant set-ups. Despite the complex appearance of the density formula, its use only requires fractions of a second on simple desktop computers such that, next to the theoretical appeal, also practicability is guaranteed.

Suggested Citation

  • Dirk Veestraeten, 2004. "The Conditional Probability Density Function for a Reflected Brownian Motion," Computational Economics, Springer;Society for Computational Economics, vol. 24(2), pages 185-207, September.
    • Handle: RePEc:kap:compec:v:24:y:2004:i:2:p:185-207
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    Cited by:

    1. Qin Hu & Yongjin Wang & Xuewei Yang, 2012. "The Hitting Time Density for a Reflected Brownian Motion," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 1-18, June.
    2. Dereudre David & Mazzonetto Sara & Roelly Sylvie, 2016. "An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers," Monte Carlo Methods and Applications, De Gruyter, vol. 22(1), pages 1-23, March.

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