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On the Laplace transforms of the first hitting times for drawdowns and drawups of diffusion-type processes

Gapeev, Pavel V., Rodosthenous, Neofytos and Chinthalapati, V.L Raju (2019) On the Laplace transforms of the first hitting times for drawdowns and drawups of diffusion-type processes. Risks, 7 (3). ISSN 2227-9091

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Identification Number: 10.3390/risks7030087

Abstract

We obtain closed-form expressions for the value of the joint Laplace transform of the running maximum and minimum of a diffusion-type process stopped at the first time at which the associated drawdown or drawup process hits a constant level before an inde- pendent exponential random time. It is assumed that the coefficients of the diffusion-type process are regular functions of the current values of its running maximum and minimum. The proof is based on the solution to the equivalent inhomogeneous ordinary differential boundary-value problem and the application of the normal-reflection conditions for the value function at the edges of the state space of the resulting three-dimensional Markov process. The result is related to the computation of probability characteristics of the take-profit and stop-loss values of a market trader during a given time period.

Item Type: Article
Additional Information: © 2019 The Authors
Divisions: Mathematics
Subjects: H Social Sciences > HG Finance
H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
Q Science > QA Mathematics
Date Deposited: 31 Jul 2019 12:51
Last Modified: 13 Sep 2019 09:45
URI: http://eprints.lse.ac.uk/id/eprint/101272

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