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A unique solution to a semilinear Black-Scholes partial differential equation for valuing multi-assets of American options

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Journal of Shanghai University (English Edition)

Abstract

In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation (PDE) was invesigated in a fixed domain for valuing two assets of American (call-max/put-min) options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.

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References

  1. Jiang Li-shang. The Mathematical Models and Methods of Valuing Option [M]. Beijing: Higher Education Press, 2002: 202–244 (in Chinese).

    Google Scholar 

  2. Ekström E. Properties of American option prices [J]. Stochastic Processes and Their Applications, 2004, 114(2): 265–278.

    Article  MATH  Google Scholar 

  3. Battauz A, Pratelli M. Optimal stopping and American options with discrete dividends and exogenous risk [J]. Mathematics and Economics, 2004, 35(2): 255–265.

    Article  MATH  Google Scholar 

  4. Kholodnyi V A. A nonlinear partial differential equation for American option in the entire domain of the state variable [J]. Nonlinear Analysis, Theory, Methods and Applications, 1997, 30(8): 5059–5070.

    Article  MATH  Google Scholar 

  5. Benth F E, Karlsen K H, Reikvam K. A semilinear Black and Scholes partial differential equation for valuing American options [J]. Finance and Stochastics, 2003, 7(3): 277–298.

    Article  MATH  Google Scholar 

  6. Jin Ye-ming. Optimal Stopping Theory and Application [M]. Changsha: National University of Defense Technology Press, 1995: 14–130 (in Chinese).

    Google Scholar 

  7. Crandall M G, Ishii H, Lions P L. User’s guide to viscosity solutions of second order partial differential equations [J]. Bulletin (New Series) of the American Mathematical Society, 1992, 27(1): 1–67.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai, 200444, P. R. China

    Luo Qing-li  (罗庆丽) & Sheng Wan-cheng  (盛万成) (Prof.)

Authors
  1. Luo Qing-li  (罗庆丽)
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  2. Sheng Wan-cheng  (盛万成)
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Corresponding author

Correspondence to Sheng Wan-cheng  (盛万成).

Additional information

Project supported by the National Natural Science Foundation of China (Grant No.10271072)

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Luo, Ql., Sheng, Wc. A unique solution to a semilinear Black-Scholes partial differential equation for valuing multi-assets of American options. J. of Shanghai Univ. 11, 344–350 (2007). https://doi.org/10.1007/s11741-007-0405-3

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  • DOI: https://doi.org/10.1007/s11741-007-0405-3

Keywords

2000 Mathematics Subject Classification

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