Journal article
C1,α regularity for degenerate parabolic equations arising from the Heston model
Communications on pure and applied analysis, Vol.22(12), pp.3430-3460
2023
DOI: 10.3934/cpaa.2023122
Abstract
This paper addresses a class of parabolic equations with boundary degeneracy associated with the Heston stochastic volatility process, a well-known degenerate mean-reverting diffusion process in mathematical finance. Solutions to our equations correspond to the pricing problem for perpetual timer options, which can be regarded as European options with random expiration time. After establishing the necessary maximum principles and the Harnack inequality, we prove local regularity up to the degenerate boundary using the dilation technique and the truncation iteration method. This result holds significant importance for degenerate parabolic equations involving the Heston operator and has practical applications in asset pricing problems.
Details
- Title: Subtitle
- C1,α regularity for degenerate parabolic equations arising from the Heston model
- Creators
- Lihe WangYaoyuan Zhang
- Resource Type
- Journal article
- Publication Details
- Communications on pure and applied analysis, Vol.22(12), pp.3430-3460
- DOI
- 10.3934/cpaa.2023122
- ISSN
- 1534-0392
- eISSN
- 1553-5258
- Language
- English
- Date published
- 2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984539756402771
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