The stability of an equation from mathematical finance without the boundary value condition
Abstract The strong degenerate parabolic equation ∂xxu+u∂yu−∂tu=f(x,y,t,u) $$ \partial _{xx}u+u\partial _{y}u-\partial _{t}u =f(x,y,t,u) $$ comes from the mathematics of finance. A kind of entropy solution is introduced. By Kružkov’s bi-variable method, the stability for entropy solutions only depen...
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SpringerOpen
2019-05-01
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| Series: | Boundary Value Problems |
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| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1207-z |
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doaj-e797afb6532d4853824c7a44300261a22020-11-25T03:04:30ZengSpringerOpenBoundary Value Problems1687-27702019-05-012019111710.1186/s13661-019-1207-zThe stability of an equation from mathematical finance without the boundary value conditionZhan Huashui0School of Applied Mathematics, Xiamen University of TechnologyAbstract The strong degenerate parabolic equation ∂xxu+u∂yu−∂tu=f(x,y,t,u) $$ \partial _{xx}u+u\partial _{y}u-\partial _{t}u =f(x,y,t,u) $$ comes from the mathematics of finance. A kind of entropy solution is introduced. By Kružkov’s bi-variable method, the stability for entropy solutions only depending on the initial value is proved. The usual boundary value condition is replaced by the regularity of the domain in a special sense.http://link.springer.com/article/10.1186/s13661-019-1207-zMathematics financeEntropy solutionKružkov’s bi-variables methodBoundary value condition |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Zhan Huashui |
| spellingShingle |
Zhan Huashui The stability of an equation from mathematical finance without the boundary value condition Boundary Value Problems Mathematics finance Entropy solution Kružkov’s bi-variables method Boundary value condition |
| author_facet |
Zhan Huashui |
| author_sort |
Zhan Huashui |
| title |
The stability of an equation from mathematical finance without the boundary value condition |
| title_short |
The stability of an equation from mathematical finance without the boundary value condition |
| title_full |
The stability of an equation from mathematical finance without the boundary value condition |
| title_fullStr |
The stability of an equation from mathematical finance without the boundary value condition |
| title_full_unstemmed |
The stability of an equation from mathematical finance without the boundary value condition |
| title_sort |
stability of an equation from mathematical finance without the boundary value condition |
| publisher |
SpringerOpen |
| series |
Boundary Value Problems |
| issn |
1687-2770 |
| publishDate |
2019-05-01 |
| description |
Abstract The strong degenerate parabolic equation ∂xxu+u∂yu−∂tu=f(x,y,t,u) $$ \partial _{xx}u+u\partial _{y}u-\partial _{t}u =f(x,y,t,u) $$ comes from the mathematics of finance. A kind of entropy solution is introduced. By Kružkov’s bi-variable method, the stability for entropy solutions only depending on the initial value is proved. The usual boundary value condition is replaced by the regularity of the domain in a special sense. |
| topic |
Mathematics finance Entropy solution Kružkov’s bi-variables method Boundary value condition |
| url |
http://link.springer.com/article/10.1186/s13661-019-1207-z |
| work_keys_str_mv |
AT zhanhuashui thestabilityofanequationfrommathematicalfinancewithouttheboundaryvaluecondition AT zhanhuashui stabilityofanequationfrommathematicalfinancewithouttheboundaryvaluecondition |
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