On the Laplace Transforms of the First Hitting Times for Drawdowns and Drawups of Diffusion-Type Processes

Pavel V. Gapeev, Neofytos Rodosthenous and V. L. Raju Chinthalapati
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Pavel V. Gapeev: Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UK
Neofytos Rodosthenous: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK
V. L. Raju Chinthalapati: Southampton Business School, University of Southampton, Southampton SO17 1BJ, UK

Risks, 2019, vol. 7, issue 3, 1-15

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 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.

Keywords: Laplace transform; first hitting time; diffusion-type process; running maximum and minimum processes; boundary-value problem; normal reflection (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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