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REGULARITY OF A DEGENERATE PARABOLIC EQUATION APPEARING IN VECER'S UNIFIED PRICING OF ASIAN OPTIONS

  • Dong, Hongjie ;
  • Kim, Seick
  • Received : 2014.06.03
  • Published : 2015.05.31

Abstract

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.

Keywords

Asian options;degenerate parabolic equation;regularity of solutions

References

  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.

Acknowledgement

Supported by : NSF, NRF