On the regularity of solutions to a nonlinear ultraparabolic equation arising in mathematical finance

Giovanna Citti; Andrea Pascucci; Sergio Polidoro

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On the regularity of solutions to a nonlinear ultraparabolic equation arising in mathematical finance

机译：数学金融中非线性超抛物方程解的正则性

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摘要

We consider the following nonlinear degenerate parabolic equation which arises in some recent problems of mathematical finance: (partial deriv)_(xx)u + u(partial deriv)_yu - (partial deriv)_tu = f. Using a harmonic analysis technique on Lie groups, we prove that, if the solution u satisfies condition (partial deriv)_xu ≠ 0 in an open set Ω is contained in R~3 and f ∈ C~∞(Ω), then u ∈ C~∞(Ω).

机译：我们考虑下面的非线性简并抛物线方程，它出现在最近的一些数学金融问题中：（偏导数）_（xx）u + u（偏导数）_yu-（偏导数）_tu = f。使用对李群的谐波分析技术，我们证明，如果解u满足开放集Ω中的条件（偏导数）_xu≠0包含在R〜3和f∈C〜∞（Ω）中，则u∈ C〜∞（Ω）。

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《Differential and integral equations》 |2001年第6期|共38页
作者
Giovanna Citti; Andrea Pascucci; Sergio Polidoro;
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正文语种 eng
中图分类微分方程、积分方程;
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1. On the regularity of solutions to a nonlinear ultraparabolic equation arising in mathematical finance [J] . Giovanna Citti, Andrea Pascucci, Sergio Polidoro Differential and integral equations . 2001,第6期

机译：数学金融中非线性超抛物方程解的正则性
2. DEGENERATE-ELLIPTIC OPERATORS IN MATHEMATICAL FINANCE AND HIGHER-ORDER REGULARITY FOR SOLUTIONS TO VARIATIONAL EQUATIONS [J] . Feehan Paul M. N., Pop Camelia A. Advances in differential equations . 2015,第3a4期

机译：数学金融中的简并椭圆算子和高阶正则解
3. THE C~α REGULARITY OF WEAK SOLUTIONS OF ULTRAPARABOLIC EQUATIONS [J] . Wendong Wang, Liqun Zhang Discrete and continuous dynamical systems . 2011,第3期

机译：超抛物方程弱解的C〜α正则性
4. ENTROPY SOLUTIONSTO A GENUINELY NONLINEAR ULTRAPARABOLIC KOLMOGOROV-TYPE EQUATION [C] . S. A SAZHENKOV Mathematical Physics Regional Conference . 2007

机译：Entropy Solutionsto真正非线性Ultlaparic Kolmogorov型方程式
5. Numerical solutions of the Hamilton-Jacobi equations arising in nonlinear H(infinity) and optimal control. [D] . Markman, Jerry. 1998

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6. A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach [O] . Taha Aziz, F. M. Mahomed -1

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7. On the regularity of solutions to a nonlinear ultraparabolic equation arising in mathematical finance [O] . S. Polidoro 2001

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On the regularity of solutions to a nonlinear ultraparabolic equation arising in mathematical finance

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