Formulas for the Laplace Transform of Stopping Times based on Drawdowns and Drawups

Details Formulas for the Laplace Transform of Stopping Times based on Drawdowns and Drawups Formulas for the Laplace Transform of Stopping Times based on Drawdowns and Drawups

2009-11-09

arxiv.org/abs/0911.1575v1

Mathematics

Probability

Scientific paper

In this work we study drawdowns and drawups of general diffusion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is defined as the current increase over its running minimum. The drawdown and the drawup are the first hitting times of the drawdown and the drawup processes respectively. In particular, we derive a closed-form formula for the Laplace transform of the probability density of the drawdown of a units when it precedes the drawup of b units. We then separately consider the special case of drifted Brownian motion, for which we derive a closed form formula for the above-mentioned density by inverting the Laplace transform. Finally, we apply the results to a problem of interest in financial risk-management and to the problem of transient signal detection and identification of two-sided changes in the drift of general diffusion processes.

Affiliated with

Also associated with

No associations

Rating

Formulas for the Laplace Transform of Stopping Times based on Drawdowns and Drawups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Formulas for the Laplace Transform of Stopping Times based on Drawdowns and Drawups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Formulas for the Laplace Transform of Stopping Times based on Drawdowns and Drawups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-659653