کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5775043 | 1413573 | 2017 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The stochastic solution to a Cauchy problem for degenerate parabolic equations
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The stochastic solution to a Cauchy problem for degenerate parabolic equations The stochastic solution to a Cauchy problem for degenerate parabolic equations](/preview/png/5775043.png)
چکیده انگلیسی
We study the stochastic solution to a Cauchy problem for a degenerate parabolic equation arising from option pricing. When the diffusion coefficient of the underlying price process is locally Hölder continuous with exponent δâ(0,1], the stochastic solution, which represents the price of a European option, is shown to be a classical solution to the Cauchy problem. This improves the standard requirement δâ¥1/2. Uniqueness results, including a Feynman-Kac formula and a comparison theorem, are established without assuming the usual linear growth condition on the diffusion coefficient. When the stochastic solution is not smooth, it is characterized as the limit of an approximating smooth stochastic solutions. In deriving the main results, we discover a new, probabilistic proof of Kotani's criterion for martingality of a one-dimensional diffusion in natural scale.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 451, Issue 1, 1 July 2017, Pages 448-472
Journal: Journal of Mathematical Analysis and Applications - Volume 451, Issue 1, 1 July 2017, Pages 448-472
نویسندگان
Xiaoshan Chen, Yu-Jui Huang, Qingshuo Song, Chao Zhu,