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European Option Pricing with Ambiguous Return Rate and Volatility

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Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

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Abstract

In this paper, we consider the problem of option pricing when return rate and volatility are ambiguous. Firstly we illustrate how to describe this ambiguous option pricing model by using set-valued differential inclusion and how to change the discussion of pricing bound problems of options into that of maximal and minimal conditional expectations. Secondly we discuss the properties of maximal and minimal conditional expectations, especially the representation theorem of maximal and minimal expectations. Finally we give the bounds of the European option pricing by using above theorems.

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References

  1. Ahmed, N.U.: Nonlinear stochastic differential inclusions on Banach space. Stoch. Anal. Appl. 12, 1–10 (1994)

    Article  MATH  Google Scholar 

  2. Aubin, J.P., Prato, G.D.: The viability theorem for stochastic differenrial inclusions. Stoch. Anal. Appl. 16, 1–15 (1998)

    Article  MATH  Google Scholar 

  3. Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–654 (1973)

    Article  Google Scholar 

  4. Chen, Z., Kulperger, R., Wei, G.: A comononic theorem of BSDEs and its applications. Stoch. Proc. Appl. 115, 41–54 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, Z., Kulperger, R.: Minmax pricing and Choquet pricing. Insur. Math. Econ. 38, 518–528 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Jung, E.J., Kim, J.H.: On set-valued stochastic integrals. Stoch. Anal. Appl. 21, 401–418 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Karoui, N., El, P.S., Quenez, M.C.: Backward stochatic differentail equation in finance. Math. Fina. 7, 1–71 (1997)

    Article  MATH  Google Scholar 

  8. Kisielewicz, M.: Set-valued stochastic integrals and stochastic inclusions. Discuss. Math. 13, 119–126 (1993)

    MathSciNet  MATH  Google Scholar 

  9. Kisielewicz, M.: Weak compactness of solution sets to stochastic differential inclusions with non-convex right-hand sides. Stoch. Anal. Appl. 23, 871–901 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Li, J., Li, S., Ogura, Y.: Strong solution of Itô type set-valued stochastic differential equation. Math. Sin. English Series 26, 1739–1748 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Shreve, S.E.: Stochastic Calculus for Finance. Springer, London (2004)

    Google Scholar 

  12. Zhang, J., Li, S., Mitoma, I., Okazaki, Y.: On set-valued stochastic integrals in an M-type 2 Banach space. J. Math. Anal. Appl. 350, 216–233 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang, J., Li, S., Mitoma, I., Okazaki, Y.: On the solution of set-valued stochastic differential equation in M-type 2 Banach space. Tohoku Math. J. 61, 417–440 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang, W., Li, S., Wang, Z., Gao, Y.: An Introduction of Set-Valued Stochastic Processes. Science Press, Beijing (2007)

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Beijing University of Technology, China

    Junfei Zhang & Shoumei Li

Authors
  1. Junfei Zhang
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  2. Shoumei Li
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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© 2011 Springer-Verlag Berlin Heidelberg

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Zhang, J., Li, S. (2011). European Option Pricing with Ambiguous Return Rate and Volatility. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_33

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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