We study a certain one-dimensional, degenerate parabolic partial differential equation with a boundary condition which arises in pricing of Asian options. Due to degeneracy of the partial differential operator and the non-smooth boundary condition, regularity of the generalized solution of such a problem remained unclear. We prove that the generalized solution of the problem is indeed a classical solution.
Bibliographical noteFunding Information:
The author is grateful to Mikhail Safonov and Jan Vecˇerˇ for very helpful discussion. The author also thanks the referee for useful comments. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-314-C00024). This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (No. R01-2008-000-20010-0). This work was supported in part by Yonsei University Research Fund of 2008-7-0246.
All Science Journal Classification (ASJC) codes
- Applied Mathematics