The maximum of Brownian motion minus a parabola
Piet Groeneboom
TL;DR
This paper derives a straightforward integral formula for the distribution of the maximum of Brownian motion minus a parabola, facilitating the computation of its density and moments for both one-sided and two-sided cases.
Contribution
It introduces a new integral representation for the distribution of the maximum of Brownian motion minus a parabola, enabling easier analysis and computation.
Findings
Provides an explicit integral formula for the distribution
Enables calculation of density and moments
Applicable to both one-sided and two-sided Brownian motion
Abstract
We derive a simple integral representation for the distribution of the maximum of Brownian motion minus a parabola, which can be used for computing the density and moments of the distribution, both for one-sided and two-sided Brownian motion.
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Taxonomy
TopicsComplex Systems and Time Series Analysis · Stochastic processes and statistical mechanics · Stochastic processes and financial applications