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Discretization error of Stochastic Integrals

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  • Masaaki Fukasawa

Abstract

Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective discretization schemes for the Euler-Maruyama approximation are constructed.

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  • Masaaki Fukasawa, 2010. "Discretization error of Stochastic Integrals," Papers 1004.2107, arXiv.org.
    • Handle: RePEc:arx:papers:1004.2107
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    References listed on IDEAS

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    1. Karandikar, Rajeeva L., 1995. "On pathwise stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 11-18, May.
    2. Konakov Valentin & Mammen Enno, 2002. "Edgeworth type expansions for Euler schemes for stochastic differential equations," Monte Carlo Methods and Applications, De Gruyter, vol. 8(3), pages 271-286, December.
    3. BALLY Vlad & TALAY Denis, 1996. "The Law of the Euler Scheme for Stochastic Differential Equations: II. Convergence Rate of the Density," Monte Carlo Methods and Applications, De Gruyter, vol. 2(2), pages 93-128, December.
    4. Takaki Hayashi & Per A. Mykland, 2005. "Evaluating Hedging Errors: An Asymptotic Approach," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 309-343, April.
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