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Articles

Approximation of Non-Lipschitz SDEs by Picard Iterations

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Pages 148-179 | Received 21 Nov 2016, Accepted 25 Jul 2018, Published online: 20 Aug 2018

References

  • Black, F., and M. Scholes. 1973. “The Pricing of Options and Corporate Liabilities.” The Journal of Political Economy 81: 637–659. doi:10.1086/260062.
  • Bouleau, N., and D. Lépingle. 1994. Numerical Methods for Stochastic Processes. United states: John Wiley and Sons.
  • Brigo, D., and F. Mercurio. 2000. “A Mixed-Up Smile.” Risk 13 (9): 123–126.
  • Dana, R. A., and J. Monique. 2003. Financial Markets in Continuous Time. Verlag Berlin Heidelberg: Springer.
  • Delbaen, F., and H. Shirakawa. 2002. “A Note on Option Pricing for Constant Elasticity of Variance Model.” Asia-Pacific Financial Markets 9 (2): 85–99. doi:10.1023/A:1022269617674.
  • Desmond, J. H., and M. Xuerong. 2013. “Convergence, Non-Negativity and Stability of a New Milstein Scheme with Applications to Finance.” Discrete and Continuous Dynamical Systems, Series B 18 (8): 2083–2100. doi:10.3934/dcdsb.2013.18.2083.
  • Dupire, B. 1997. “Pricing and Hedging with Smiles. Mathematics of Derivative Securities.” Cambridge University Pressure 15: 103–111.
  • Friedman, A. 1975. Stochastic Differential Equations And Applications. New York: Dover Books on Mathematics.
  • Funahashi, H. 2014. “A Chaos Expansion Approach under Hybrid Volatility Models.” Quantitative Finance 14 (11): 1923–1936. doi:10.1080/14697688.2013.872283.
  • Hull, J., and A. White. 1987. “The Pricing of Options on Assets with Stochastic Volatilities.” Journal of Finance 42: 281–300. doi:10.1111/j.1540-6261.1987.tb02568.x.
  • Neuenkirch, A., and L. Szpruch. 2014. “First Order Strong Approximations of Scalar SDEs Defined in a Domain.” Numerische Mathematik 1–34.
  • Kijima, M., and H. Funahashi. 2015. “A Chaos Expansion Approach for the Pricing of Contingent Claims.” Journal of Computational Finance 18 (3): 27–58. doi:10.21314/JCF.2015.299.
  • Kloeden, P. E., and E. Platen. 1992. “Numerical Solution of Stochastic Differential Equations.” In Stochastic Modelling and Applied Probability, 23.Verlag Berlin Heidelberg:Springer
  • Lindsay, A. E., and D. R. Brecher. 2012. “Simulation of the CEV Process and the Local Martingale Property.” Mathematics and Computers in Simulation 82 (5): 868–878. doi:10.1016/j.matcom.2011.12.006.
  • Nualart, D. 2006. “The Malliavin Calculus and Related Topics.” In Probability, Its Applications. Berlin Heidelberg:Springer.
  • Mehrdoust, F., S. Babaei, and S. Fallah. 2015. “Efficient Monte Carlo Option Pricing under CEV Model.” Communications in Statistics - Simulation and Computation. doi:10.1080/03610918.2015.1040497.
  • Schroder, M. 1989. “Computing the Constant Elasticity of Variance Option Pricing Formula.” The Journal of Finance 44 (1): 211–219. doi:10.1111/j.1540-6261.1989.tb02414.x.

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