The Hitting Time Density for a Reflected Brownian Motion
Computational Economics
Analytical and stochastic modelling of battery cell dynamics
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
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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.