On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function. (9th September 2015)

• Record Type: Journal Article
• Authors: Guillaume, Tristan
• Other Names: Lai Dejian Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2015(2015)
• Publication Date: 2015-09-09
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2015/391681
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. Various combinations of downward and upward steps are handled. Numerical computation of the survival probability is done quasi-instantaneously and with utmost precision. The sensitivity of the survival probability to the number and the ordering of the steps in the boundary is analyzed.