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

Gapeev, Pavel; 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), pp. 1-15. ISSN 2227-9091 [Article]

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Abstract or Description

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 independent 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

Keywords:

Laplace transform; first hitting time; diffusion-type process; running maximum and minimum processes; boundary-value problem; normal reflection.

Departments, Centres and Research Units:

Computing

Dates:

DateEvent
30 July 2019Accepted
5 August 2019Published

Item ID:

28409

Date Deposited:

05 May 2020 11:10

Last Modified:

05 May 2020 11:10

Peer Reviewed:

Yes, this version has been peer-reviewed.

URI:

http://research.gold.ac.uk/id/eprint/28409

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