 On the Laplace transforms of the first hitting times for drawdowns and drawups of diffusion-type processesPavel V. Gapeev, Neofytos Rodosthenous and V.L Raju Chinthalapati LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library 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. JEL-codes: F3 G3 G32 (search for similar items in EconPapers) Published in Risks, 5, August, 2019, 7(3). ISSN: 2227-9091 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:101272 Access Statistics for this paper More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC. |
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