First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries
Abstract The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian moti...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yu, Zhen [verfasserIn] Tian, Mao Zai [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
Boundary non-crossing probability |
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| Anmerkung: |
© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2024 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mathematica sinica - Springer Berlin Heidelberg, 1985, 40(2024), 6 vom: 15. März, Seite 1505-1520 |
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| Übergeordnetes Werk: |
volume:40 ; year:2024 ; number:6 ; day:15 ; month:03 ; pages:1505-1520 |
| Links: |
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| DOI / URN: |
10.1007/s10114-024-1090-0 |
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| Katalog-ID: |
SPR056301669 |
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| 520 | |a Abstract The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian motion with two-sided piecewise continuous boundaries which may have some points of discontinuity. Approximations are used to obtain a simplified formula for estimating the first passage density. Moreover, the results are also generalized to the case of two-sided general nonlinear boundaries. Simulations can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density. | ||
| 650 | 4 | |a Boundary non-crossing probability |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a first density passage density |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a two-sided piecewise continuous boundaries |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Brownian motion |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Tian, Mao Zai |e verfasserin |4 aut | |
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10.1007/s10114-024-1090-0 doi (DE-627)SPR056301669 (SPR)s10114-024-1090-0-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Yu, Zhen verfasserin aut First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2024 Abstract The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian motion with two-sided piecewise continuous boundaries which may have some points of discontinuity. Approximations are used to obtain a simplified formula for estimating the first passage density. Moreover, the results are also generalized to the case of two-sided general nonlinear boundaries. Simulations can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density. Boundary non-crossing probability (dpeaa)DE-He213 first density passage density (dpeaa)DE-He213 two-sided piecewise continuous boundaries (dpeaa)DE-He213 Brownian motion (dpeaa)DE-He213 Tian, Mao Zai verfasserin aut Enthalten in Acta mathematica sinica Springer Berlin Heidelberg, 1985 40(2024), 6 vom: 15. März, Seite 1505-1520 (DE-627)312226470 (DE-600)2011055-8 1439-7617 nnns volume:40 year:2024 number:6 day:15 month:03 pages:1505-1520 https://dx.doi.org/10.1007/s10114-024-1090-0 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 40 2024 6 15 03 1505-1520 |
| spelling |
10.1007/s10114-024-1090-0 doi (DE-627)SPR056301669 (SPR)s10114-024-1090-0-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Yu, Zhen verfasserin aut First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2024 Abstract The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian motion with two-sided piecewise continuous boundaries which may have some points of discontinuity. Approximations are used to obtain a simplified formula for estimating the first passage density. Moreover, the results are also generalized to the case of two-sided general nonlinear boundaries. Simulations can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density. Boundary non-crossing probability (dpeaa)DE-He213 first density passage density (dpeaa)DE-He213 two-sided piecewise continuous boundaries (dpeaa)DE-He213 Brownian motion (dpeaa)DE-He213 Tian, Mao Zai verfasserin aut Enthalten in Acta mathematica sinica Springer Berlin Heidelberg, 1985 40(2024), 6 vom: 15. März, Seite 1505-1520 (DE-627)312226470 (DE-600)2011055-8 1439-7617 nnns volume:40 year:2024 number:6 day:15 month:03 pages:1505-1520 https://dx.doi.org/10.1007/s10114-024-1090-0 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 40 2024 6 15 03 1505-1520 |
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10.1007/s10114-024-1090-0 doi (DE-627)SPR056301669 (SPR)s10114-024-1090-0-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Yu, Zhen verfasserin aut First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2024 Abstract The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian motion with two-sided piecewise continuous boundaries which may have some points of discontinuity. Approximations are used to obtain a simplified formula for estimating the first passage density. Moreover, the results are also generalized to the case of two-sided general nonlinear boundaries. Simulations can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density. Boundary non-crossing probability (dpeaa)DE-He213 first density passage density (dpeaa)DE-He213 two-sided piecewise continuous boundaries (dpeaa)DE-He213 Brownian motion (dpeaa)DE-He213 Tian, Mao Zai verfasserin aut Enthalten in Acta mathematica sinica Springer Berlin Heidelberg, 1985 40(2024), 6 vom: 15. März, Seite 1505-1520 (DE-627)312226470 (DE-600)2011055-8 1439-7617 nnns volume:40 year:2024 number:6 day:15 month:03 pages:1505-1520 https://dx.doi.org/10.1007/s10114-024-1090-0 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 40 2024 6 15 03 1505-1520 |
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10.1007/s10114-024-1090-0 doi (DE-627)SPR056301669 (SPR)s10114-024-1090-0-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Yu, Zhen verfasserin aut First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2024 Abstract The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian motion with two-sided piecewise continuous boundaries which may have some points of discontinuity. Approximations are used to obtain a simplified formula for estimating the first passage density. Moreover, the results are also generalized to the case of two-sided general nonlinear boundaries. Simulations can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density. Boundary non-crossing probability (dpeaa)DE-He213 first density passage density (dpeaa)DE-He213 two-sided piecewise continuous boundaries (dpeaa)DE-He213 Brownian motion (dpeaa)DE-He213 Tian, Mao Zai verfasserin aut Enthalten in Acta mathematica sinica Springer Berlin Heidelberg, 1985 40(2024), 6 vom: 15. März, Seite 1505-1520 (DE-627)312226470 (DE-600)2011055-8 1439-7617 nnns volume:40 year:2024 number:6 day:15 month:03 pages:1505-1520 https://dx.doi.org/10.1007/s10114-024-1090-0 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 40 2024 6 15 03 1505-1520 |
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Yu, Zhen |
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Yu, Zhen ddc 510 bkl 31.00 misc Boundary non-crossing probability misc first density passage density misc two-sided piecewise continuous boundaries misc Brownian motion First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries |
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510 VZ 31.00 bkl First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries Boundary non-crossing probability (dpeaa)DE-He213 first density passage density (dpeaa)DE-He213 two-sided piecewise continuous boundaries (dpeaa)DE-He213 Brownian motion (dpeaa)DE-He213 |
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ddc 510 bkl 31.00 misc Boundary non-crossing probability misc first density passage density misc two-sided piecewise continuous boundaries misc Brownian motion |
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ddc 510 bkl 31.00 misc Boundary non-crossing probability misc first density passage density misc two-sided piecewise continuous boundaries misc Brownian motion |
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First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries |
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First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries |
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first passage density of brownian motion with two-sided piecewise linear boundaries |
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First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries |
| abstract |
Abstract The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian motion with two-sided piecewise continuous boundaries which may have some points of discontinuity. Approximations are used to obtain a simplified formula for estimating the first passage density. Moreover, the results are also generalized to the case of two-sided general nonlinear boundaries. Simulations can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density. © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2024 |
| abstractGer |
Abstract The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian motion with two-sided piecewise continuous boundaries which may have some points of discontinuity. Approximations are used to obtain a simplified formula for estimating the first passage density. Moreover, the results are also generalized to the case of two-sided general nonlinear boundaries. Simulations can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density. © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2024 |
| abstract_unstemmed |
Abstract The first passage time has many applications in fields like finance, econometrics, statistics, and biology. However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian motion with two-sided piecewise continuous boundaries which may have some points of discontinuity. Approximations are used to obtain a simplified formula for estimating the first passage density. Moreover, the results are also generalized to the case of two-sided general nonlinear boundaries. Simulations can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density. © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2024 |
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First Passage Density of Brownian Motion with Two-sided Piecewise Linear Boundaries |
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https://dx.doi.org/10.1007/s10114-024-1090-0 |
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Tian, Mao Zai |
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Tian, Mao Zai |
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| doi_str |
10.1007/s10114-024-1090-0 |
| up_date |
2024-07-03T21:31:17.903Z |
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However, explicit formulas for the first passage density have only been obtained for a few cases. This paper derives an explicit formula for the first passage density of Brownian motion with two-sided piecewise continuous boundaries which may have some points of discontinuity. Approximations are used to obtain a simplified formula for estimating the first passage density. Moreover, the results are also generalized to the case of two-sided general nonlinear boundaries. 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