A novel numerical scheme for a time fractional Black–Scholes equation
This paper consists of two parts. On one hand, the regularity of the solution of the time-fractional Black–Scholes equation is investigated. On the other hand, to overcome the difficulty of initial layer, a modified L 1 time discretization is presented based on a change of variable. And the spatial...
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| Veröffentlicht in: | Journal of applied mathematics & computing 2021-06, Vol.66 (1-2), p.853-870 |
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| container_title | Journal of applied mathematics & computing |
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| creator | She, Mianfu Li, Lili Tang, Renxuan Li, Dongfang |
| description | This paper consists of two parts. On one hand, the regularity of the solution of the time-fractional Black–Scholes equation is investigated. On the other hand, to overcome the difficulty of initial layer, a modified
L
1 time discretization is presented based on a change of variable. And the spatial discretization is done by using the Chebyshev Galerkin method. Optimal error estimates of the fully-discrete scheme are obtained. Finally, several numerical results are given to confirm the theoretical results. |
| doi_str_mv | 10.1007/s12190-020-01467-9 |
| format | Article |
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L
1 time discretization is presented based on a change of variable. And the spatial discretization is done by using the Chebyshev Galerkin method. Optimal error estimates of the fully-discrete scheme are obtained. Finally, several numerical results are given to confirm the theoretical results.</description><identifier>ISSN: 1598-5865</identifier><identifier>EISSN: 1865-2085</identifier><identifier>DOI: 10.1007/s12190-020-01467-9</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied mathematics ; Black-Scholes equation ; Chebyshev approximation ; Computational Mathematics and Numerical Analysis ; Discretization ; Galerkin method ; Mathematical and Computational Engineering ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Original Research ; Theory of Computation</subject><ispartof>Journal of applied mathematics & computing, 2021-06, Vol.66 (1-2), p.853-870</ispartof><rights>Korean Society for Informatics and Computational Applied Mathematics 2020</rights><rights>Korean Society for Informatics and Computational Applied Mathematics 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-b8db0678c84c0ff9cc6ffd79d780dcb4e794fbd8f0f38f978779179f2579ba403</citedby><cites>FETCH-LOGICAL-c319t-b8db0678c84c0ff9cc6ffd79d780dcb4e794fbd8f0f38f978779179f2579ba403</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12190-020-01467-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12190-020-01467-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>She, Mianfu</creatorcontrib><creatorcontrib>Li, Lili</creatorcontrib><creatorcontrib>Tang, Renxuan</creatorcontrib><creatorcontrib>Li, Dongfang</creatorcontrib><title>A novel numerical scheme for a time fractional Black–Scholes equation</title><title>Journal of applied mathematics & computing</title><addtitle>J. Appl. Math. Comput</addtitle><description>This paper consists of two parts. On one hand, the regularity of the solution of the time-fractional Black–Scholes equation is investigated. On the other hand, to overcome the difficulty of initial layer, a modified
L
1 time discretization is presented based on a change of variable. And the spatial discretization is done by using the Chebyshev Galerkin method. Optimal error estimates of the fully-discrete scheme are obtained. Finally, several numerical results are given to confirm the theoretical results.</description><subject>Applied mathematics</subject><subject>Black-Scholes equation</subject><subject>Chebyshev approximation</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Discretization</subject><subject>Galerkin method</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Original Research</subject><subject>Theory of Computation</subject><issn>1598-5865</issn><issn>1865-2085</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9UMFKxDAQDaLguvoDngKeo0naNMlxXXQVFjyo55Cmidu1bXaTVvDmP_iHfompFbwJM8ww896b4QFwTvAlwZhfRUKJxAjTlCQvOJIHYEZEwRDFgh2mnkmBWBocg5MYtxgXXGI5A6sF7PybbWA3tDbURjcwmo1tLXQ-QA37emyDNn3tu7S8brR5_fr4fDQb39gI7X7Q4-oUHDndRHv2W-fg-fbmaXmH1g-r--VijUxGZI9KUZXptDAiN9g5aUzhXMVlxQWuTJlbLnNXVsJhlwknueBcEi4dZVyWOsfZHFxMurvg94ONvdr6IaTPoqKMskKkGFF0QpngYwzWqV2oWx3eFcFqNExNhqlkmPoxTMlEyiZSTODuxYY_6X9Y34u0bt8</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>She, Mianfu</creator><creator>Li, Lili</creator><creator>Tang, Renxuan</creator><creator>Li, Dongfang</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20210601</creationdate><title>A novel numerical scheme for a time fractional Black–Scholes equation</title><author>She, Mianfu ; Li, Lili ; Tang, Renxuan ; Li, Dongfang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-b8db0678c84c0ff9cc6ffd79d780dcb4e794fbd8f0f38f978779179f2579ba403</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Applied mathematics</topic><topic>Black-Scholes equation</topic><topic>Chebyshev approximation</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Discretization</topic><topic>Galerkin method</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Original Research</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>She, Mianfu</creatorcontrib><creatorcontrib>Li, Lili</creatorcontrib><creatorcontrib>Tang, Renxuan</creatorcontrib><creatorcontrib>Li, Dongfang</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of applied mathematics & computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>She, Mianfu</au><au>Li, Lili</au><au>Tang, Renxuan</au><au>Li, Dongfang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A novel numerical scheme for a time fractional Black–Scholes equation</atitle><jtitle>Journal of applied mathematics & computing</jtitle><stitle>J. Appl. Math. Comput</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>66</volume><issue>1-2</issue><spage>853</spage><epage>870</epage><pages>853-870</pages><issn>1598-5865</issn><eissn>1865-2085</eissn><abstract>This paper consists of two parts. On one hand, the regularity of the solution of the time-fractional Black–Scholes equation is investigated. On the other hand, to overcome the difficulty of initial layer, a modified
L
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| issn | 1598-5865 1865-2085 |
| language | eng |
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| subjects | Applied mathematics Black-Scholes equation Chebyshev approximation Computational Mathematics and Numerical Analysis Discretization Galerkin method Mathematical and Computational Engineering Mathematics Mathematics and Statistics Mathematics of Computing Original Research Theory of Computation |
| title | A novel numerical scheme for a time fractional Black–Scholes equation |
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