Sobolev estimates and inverse Hölder estimates on a class of non-divergence variation-inequality problem arising in American option pricing
We studied the Sobolev estimates and inverse Hölder estimates for a class of variational inequality problems involving divergence-type parabolic operator structures. These problems arise from the valuation analysis of American contingent claim problems. First, we analyzed the uniform continuity of t...
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| Language: | English |
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AIMS Press
2024-11-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024277 |
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| author | Kaiyu Zhang |
| author_facet | Kaiyu Zhang |
| author_sort | Kaiyu Zhang |
| collection | DOAJ |
| description | We studied the Sobolev estimates and inverse Hölder estimates for a class of variational inequality problems involving divergence-type parabolic operator structures. These problems arise from the valuation analysis of American contingent claim problems. First, we analyzed the uniform continuity of the spatially averaged operator with respect to time in a spherical region and the Sobolev estimates for solutions of the variational inequality. Second, by using spatial and temporal truncation, we obtained the Caccioppoli estimate for the variational inequality and consequently derived the inverse Hölder estimate for the solutions. |
| format | Article |
| id | doaj-art-8584bdb5be3a4fc3a72d4d8db01a2324 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-8584bdb5be3a4fc3a72d4d8db01a23242025-01-23T07:53:00ZengAIMS PressElectronic Research Archive2688-15942024-11-0132115975598710.3934/era.2024277Sobolev estimates and inverse Hölder estimates on a class of non-divergence variation-inequality problem arising in American option pricingKaiyu Zhang0School of Accounting, Jilin Province Economic Management Cadre College, Changchun, Jilin 130012, ChinaWe studied the Sobolev estimates and inverse Hölder estimates for a class of variational inequality problems involving divergence-type parabolic operator structures. These problems arise from the valuation analysis of American contingent claim problems. First, we analyzed the uniform continuity of the spatially averaged operator with respect to time in a spherical region and the Sobolev estimates for solutions of the variational inequality. Second, by using spatial and temporal truncation, we obtained the Caccioppoli estimate for the variational inequality and consequently derived the inverse Hölder estimate for the solutions.https://www.aimspress.com/article/doi/10.3934/era.2024277variation-inequality problemsnon-divergence parabolic operatorsobolev estimateinverse hölder estimate |
| spellingShingle | Kaiyu Zhang Sobolev estimates and inverse Hölder estimates on a class of non-divergence variation-inequality problem arising in American option pricing Electronic Research Archive variation-inequality problems non-divergence parabolic operator sobolev estimate inverse hölder estimate |
| title | Sobolev estimates and inverse Hölder estimates on a class of non-divergence variation-inequality problem arising in American option pricing |
| title_full | Sobolev estimates and inverse Hölder estimates on a class of non-divergence variation-inequality problem arising in American option pricing |
| title_fullStr | Sobolev estimates and inverse Hölder estimates on a class of non-divergence variation-inequality problem arising in American option pricing |
| title_full_unstemmed | Sobolev estimates and inverse Hölder estimates on a class of non-divergence variation-inequality problem arising in American option pricing |
| title_short | Sobolev estimates and inverse Hölder estimates on a class of non-divergence variation-inequality problem arising in American option pricing |
| title_sort | sobolev estimates and inverse holder estimates on a class of non divergence variation inequality problem arising in american option pricing |
| topic | variation-inequality problems non-divergence parabolic operator sobolev estimate inverse hölder estimate |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024277 |
| work_keys_str_mv | AT kaiyuzhang sobolevestimatesandinverseholderestimatesonaclassofnondivergencevariationinequalityproblemarisinginamericanoptionpricing |