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On the drawdowns and drawups in diffusion-type models with running maxima and minima

Gapeev, Pavel V. and Rodosthenous, Neofytos (2015) On the drawdowns and drawups in diffusion-type models with running maxima and minima. Journal of Mathematical Analysis and Applications, 434 (1). pp. 413-431. ISSN 0022-247X

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Identification Number: 10.1016/j.jmaa.2015.09.013


We obtain closed-form expressions for the values of joint Laplace transforms of the running maximum and minimum of a diffusion-type process stopped at the first time at which the associated drawdown and drawup processes hit constant levels. It is assumed that the coefficients of the diffusion-type process are regular functions of the running values of the process itself, its maximum and minimum, as well as its maximum drawdown and maximum drawup processes. The proof is based on the solution to the equivalent boundary-value problems and application of the normal-reflection conditions for the value functions at the edges of the state space of the resulting five-dimensional Markov process. We show that the joint Laplace transforms represent linear combinations of solutions to the systems of first-order partial differential equations arising from the application of the normal-reflection conditions.

Item Type: Article
Official URL:
Additional Information: © 2015 Elsevier Inc.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 10 Sep 2015 14:15
Last Modified: 12 Jun 2024 06:51
Funders: Suntory and Toyota International Centres for Economics and Related Disciplines

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