Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155945 | Stochastic Processes and their Applications | 2009 | 16 Pages |
Abstract
This paper studies drawdown and drawup processes in a general diffusion model. The main result is a formula for the joint distribution of the running minimum and the running maximum of the process stopped at the time of the first drop of size aa. As a consequence, we obtain the probabilities that a drawdown of size aa precedes a drawup of size bb and vice versa. The results are applied to several examples of diffusion processes, such as drifted Brownian motion, Ornstein–Uhlenbeck process, and Cox–Ingersoll–Ross process.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Libor Pospisil, Jan Vecer, Olympia Hadjiliadis,