On the Laplace Transforms of the First Hitting Times for Drawdowns and Drawups of Diffusion-Type Processes
Abstract
:1. Introduction
2. Preliminaries
2.1. Formulation of the Problem
2.2. The Boundary-Value Problems
3. Solutions to the Boundary-Value Problem
3.1. The General Solution of the Ordinary Differential Equation
3.2. The Solution to the Boundary-Value Problem
3.3. Some Examples
4. The Result and Proof
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Gapeev, P.V.; Rodosthenous, N.; Chinthalapati, V.L.R. On the Laplace Transforms of the First Hitting Times for Drawdowns and Drawups of Diffusion-Type Processes. Risks 2019, 7, 87. https://doi.org/10.3390/risks7030087
Gapeev PV, Rodosthenous N, Chinthalapati VLR. On the Laplace Transforms of the First Hitting Times for Drawdowns and Drawups of Diffusion-Type Processes. Risks. 2019; 7(3):87. https://doi.org/10.3390/risks7030087
Chicago/Turabian StyleGapeev, Pavel V., Neofytos Rodosthenous, and V. L. Raju Chinthalapati. 2019. "On the Laplace Transforms of the First Hitting Times for Drawdowns and Drawups of Diffusion-Type Processes" Risks 7, no. 3: 87. https://doi.org/10.3390/risks7030087