대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제52권3호
  • /
  • Pages.947-953
  • /
  • 2015
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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REGULARITY OF A DEGENERATE PARABOLIC EQUATION APPEARING IN VECER'S UNIFIED PRICING OF ASIAN OPTIONS

  • Dong, Hongjie (Division of Applied Mathematics Brown University) ;
  • Kim, Seick (Department of Mathematics Yonsei University)
  • 투고 : 2014.06.03
  • 발행 : 2015.05.31
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초록

Vecer derived a degenerate parabolic equation characterizing the price of Asian options with generally sampled average. It is well understood that there exists a unique probabilistic solution to Vecer's PDE but it remained unclear whether the probabilistic solution is a classical solution. We prove that the probabilistic solution to Vecer's PDE is indeed regular.

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참고문헌

  1. S. Kim, On a degenerate parabolic equation arising in pricing of Asian options, J. Math. Anal. Appl. 351 (2009), no. 1, 326-333. https://doi.org/10.1016/j.jmaa.2008.10.019
  2. N. V. Krylov, Introduction to the Theory of Diffusion Processes, American Mathematical Society, Providence, RI, 1995.
  3. N. V. Krylov, Lectures on Elliptic and Parabolic Equations in Holder Spaces, American Mathematical Society, Providence, RI, 1996.
  4. J. Vecer, Unified Asian Pricing, Risk 15 (2002), no. 6, 113-116.