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On a non-classical invariance principle

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  • Davydov, Youri
  • Rotar, Vladimir

Abstract

We consider the invariance principle without the classical condition of asymptotic negligibility of individual terms. More precisely, let r.v.'s {[xi]nj} and {[eta]nj} be such that and the r.v.'s {[eta]nj} are normal. We set Let Xn(t) and Yn(t) be continuous piecewise linear (or polygonal) random functions with vertices at (tkn,Skn) and (tkn,Ykn), respectively, and let Pn and Qn be the respective distributions of the processes Xn(t) and Yn(t) in . The goal of the present paper is to establish necessary and sufficient conditions for convergence of Pn-Qn to zero measure not involving the condition of the asymptotic negligibility of the r.v.'s {[xi]nj} and {[eta]nj}.

Suggested Citation

  • Davydov, Youri & Rotar, Vladimir, 2008. "On a non-classical invariance principle," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2031-2038, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:14:p:2031-2038
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    Cited by:

    1. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2020. "Option Pricing Incorporating Factor Dynamics in Complete Markets," JRFM, MDPI, vol. 13(12), pages 1-33, December.
    2. Kim, Y.S. & Stoyanov, S. & Rachev, S. & Fabozzi, F., 2016. "Multi-purpose binomial model: Fitting all moments to the underlying geometric Brownian motion," Economics Letters, Elsevier, vol. 145(C), pages 225-229.
    3. Stoyan V. Stoyanov & Yong Shin Kim & Svetlozar T. Rachev & Frank J. Fabozzi, 2017. "Option pricing for Informed Traders," Papers 1711.09445, arXiv.org.
    4. Kim, Young Shin & Stoyanov, Stoyan & Rachev, Svetlozar & Fabozzi, Frank J., 2019. "Enhancing binomial and trinomial equity option pricing models," Finance Research Letters, Elsevier, vol. 28(C), pages 185-190.
    5. Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    6. Svetlozar Rachev & Stoyan Stoyanov & Frank J. Fabozzi, 2017. "Behavioral Finance Option Pricing Formulas Consistent with Rational Dynamic Asset Pricing," Papers 1710.03205, arXiv.org.

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