Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775043 | Journal of Mathematical Analysis and Applications | 2017 | 25 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xiaoshan Chen, Yu-Jui Huang, Qingshuo Song, Chao Zhu,