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Functional CLTs for subordinated L\'evy models in physics, finance, and econometrics

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  • Andreas S{o}jmark
  • Fabrice Wunderlich

Abstract

We present a simple unifying treatment of a broad class of applications from statistical mechanics, econometrics, mathematical finance, and insurance mathematics, where (possibly subordinated) L\'evy noise arises as a scaling limit of some form of continuous-time random walk (CTRW). For each application, it is natural to rely on weak convergence results for stochastic integrals on Skorokhod space in Skorokhod's J1 or M1 topologies. As compared to earlier and entirely separate works, we are able to give a more streamlined account while also allowing for greater generality and providing important new insights. For each application, we first elucidate how the fundamental conclusions for J1 convergent CTRWs emerge as special cases of the same general principles, and we then illustrate how the specific settings give rise to different results for strictly M1 convergent CTRWs.

Suggested Citation

  • Andreas S{o}jmark & Fabrice Wunderlich, 2023. "Functional CLTs for subordinated L\'evy models in physics, finance, and econometrics," Papers 2312.15119, arXiv.org, revised Jan 2024.
    • Handle: RePEc:arx:papers:2312.15119
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    References listed on IDEAS

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    1. Chan, Ngai Hang & Zhang, Rong-Mao, 2009. "Quantile inference for near-integrated autoregressive time series under infinite variance and strong dependence," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4124-4148, December.
    2. Caner, Mehmet, 1997. "Weak Convergence to a Matrix Stochastic Integral with Stable Processes," Econometric Theory, Cambridge University Press, vol. 13(4), pages 506-528, February.
    3. Davis, Richard A. & Song, Li, 2012. "Functional convergence of stochastic integrals with application to statistical inference," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 725-757.
    4. S. James Press, 1967. "A Compound Events Model for Security Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 317-317.
    5. Darrell Duffie & Philip Protter, 1992. "From Discrete‐ to Continuous‐Time Finance: Weak Convergence of the Financial Gain Process1," Mathematical Finance, Wiley Blackwell, vol. 2(1), pages 1-15, January.
    6. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    7. Straka, P. & Henry, B.I., 2011. "Lagging and leading coupled continuous time random walks, renewal times and their joint limits," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 324-336, February.
    8. Corina D. Constantinescu & Jorge M. Ramirez & Wei R. Zhu, 2019. "An application of fractional differential equations to risk theory," Finance and Stochastics, Springer, vol. 23(4), pages 1001-1024, October.
    9. Scalas, Enrico & Viles, Noèlia, 2014. "A functional limit theorem for stochastic integrals driven by a time-changed symmetric α-stable Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 385-410.
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