On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function
This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. Various combinations of downward and upward steps are handled. Numerical computation of the survi...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2015/391681 |
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| _version_ | 1832546635218944000 |
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| author | Tristan Guillaume |
| author_facet | Tristan Guillaume |
| author_sort | Tristan Guillaume |
| collection | DOAJ |
| description | This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. Various combinations of downward and upward steps are handled. Numerical computation of the survival probability is done quasi-instantaneously and with utmost precision. The sensitivity of the survival probability to the number and the ordering of the steps in the boundary is analyzed. |
| format | Article |
| id | doaj-art-db36565ae35541c8b0958ddfcf7eb8a5 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-db36565ae35541c8b0958ddfcf7eb8a52025-02-03T06:47:56ZengWileyJournal of Probability and Statistics1687-952X1687-95382015-01-01201510.1155/2015/391681391681On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step FunctionTristan Guillaume0Université de Cergy-Pontoise, Laboratoire Thema, 33 boulevard du port, 95011 Cergy-Pontoise Cedex, FranceThis paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. Various combinations of downward and upward steps are handled. Numerical computation of the survival probability is done quasi-instantaneously and with utmost precision. The sensitivity of the survival probability to the number and the ordering of the steps in the boundary is analyzed.http://dx.doi.org/10.1155/2015/391681 |
| spellingShingle | Tristan Guillaume On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function Journal of Probability and Statistics |
| title | On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function |
| title_full | On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function |
| title_fullStr | On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function |
| title_full_unstemmed | On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function |
| title_short | On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function |
| title_sort | on the computation of the survival probability of brownian motion with drift in a closed time interval when the absorbing boundary is a step function |
| url | http://dx.doi.org/10.1155/2015/391681 |
| work_keys_str_mv | AT tristanguillaume onthecomputationofthesurvivalprobabilityofbrownianmotionwithdriftinaclosedtimeintervalwhentheabsorbingboundaryisastepfunction |