Linear programming and the inverse method of images

Zipkin, Paul

doi:10.1007/s10479-012-1249-4

Search citation statements

Order By: Relevance

Paper Sections

Select...

The First Passage Time Problem and Fredholm Intgral Equations1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Other1

Article1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Apart from the well known Bachelier-Lévy formula for linear boundaries, there are closed solutions for the square-root boundary (see e.g., [Bre67], [RSS84] and [NFK99]) and for the quadratic boundary in terms of Airy functions (see e.g., [Sal88] and [Gro89]). One method for producing analytically solvable examples is the method of images, see [Ler86], but its use for treating given barriers is limited, see e.g., [LRD02], [Zip13].…”

Section: The First Passage Time Problem and Fredholm Intgral Equationsmentioning

confidence: 99%

Uniqueness of First Passage Time Distributions via Fredholm Integral Equations

Christensen¹,

Fischer²,

Hallmann³

2023

Preprint

View full text Add to dashboard Cite

Let W be a standard Brownian motion with W 0 = 0 and let b : R + → R be a continuous function with b(0) > 0. The first passage time (from below) is then defined asIt is well-known that the distribution F of τ satisfies a set of Fredholm equations of the first kind, which is used, for example, as a starting point for numerical approaches. For this, it is fundamental that the Fredholm equations have a unique solution. In this article, we prove this in a general setting using analytical methods.

show abstract