On a degenerate parabolic equation arising in pricing of Asian options

Seick Kim

doi:10.1016/j.jmaa.2008.10.019

On a degenerate parabolic equation arising in pricing of Asian options

Seick Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	326-333
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	351
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2008.10.019
Publication status	Published - 2009 Mar 1

Bibliographical note

Funding 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

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2008.10.019

Cite this

@article{7d4fd8e7213f41f9a82e0c9c4e123cee,

title = "On a degenerate parabolic equation arising in pricing of Asian options",

abstract = "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.",

author = "Seick Kim",

note = "Funding 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.",

year = "2009",

month = mar,

day = "1",

doi = "10.1016/j.jmaa.2008.10.019",

language = "English",

volume = "351",

pages = "326--333",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - On a degenerate parabolic equation arising in pricing of Asian options

AU - Kim, Seick

N1 - Funding 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.

PY - 2009/3/1

Y1 - 2009/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=56549112726&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56549112726&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2008.10.019

DO - 10.1016/j.jmaa.2008.10.019

M3 - Article

AN - SCOPUS:56549112726

SN - 0022-247X

VL - 351

SP - 326

EP - 333

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

On a degenerate parabolic equation arising in pricing of Asian options

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this