Computational Economics

, Volume 24, Issue 2, pp 185–207

The Conditional Probability Density Function for a Reflected Brownian Motion

Authors

  • Dirk Veestraeten
    • Faculty of Economics and Econometrics, Department of EconomicsUniversity of Amsterdam
Article

DOI: 10.1023/B:CSEM.0000049491.13935.af

Cite this article as:
Veestraeten, D. Computational Economics (2004) 24: 185. doi:10.1023/B:CSEM.0000049491.13935.af

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.

asset pricesBrownian motionGreen's functionsLaplace transformreflecting boundariestransition density
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© Kluwer Academic Publishers 2004