| Autor: |
Pavel V. Gapeev, Neofytos Rodosthenous, V. L. Raju Chinthalapati |
| Jazyk: |
angličtina |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Risks, Vol 7, Iss 3, p 87 (2019) |
| Druh dokumentu: |
article |
| ISSN: |
2227-9091 |
| DOI: |
10.3390/risks7030087 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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