Inverse method of images

Violet S.F. Lo; Gareth O. Roberts; Henry E. Daniels

doi:bj/1078951089

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Home > Journals > Bernoulli > Volume 8 > Issue 1 > Article

February 2002 Inverse method of images

Violet S.F. Lo, Gareth O. Roberts, Henry E. Daniels

Author Affiliations +

Violet S.F. Lo,¹ Gareth O. Roberts,² Henry E. Daniels²
¹Deutsche Bank AG, 1 Great Winchester Street
²Department of Mathematics and Statistics, Lancaster University

Bernoulli 8(1): 53-80 (February 2002).

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Abstract

We consider the problem of approximating the density of the time at which a Brownian path first crosses a curved boundary in cases where the exact density is not known or is difficult to compute. Approximation methods which involve the use of images will be proposed. These methods can be used not only for one-sided boundaries but also for the case of two-sided boundaries; not only for concave boundaries but also for convex boundaries. The square root boundary and parabolic boundary provide examples for numerical comparisons of the approximation methods.