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Infinitesimal generators for two-dimensional Lévy process-driven hypothesis testing

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  • Michael Roberts

    (North Dakota State University)

  • Indranil SenGupta

    (North Dakota State University)

Abstract

In this paper, we present the testing of four hypotheses on two streams of observations that are driven by Lévy processes. This is applicable for sequential decision making on the state of two-sensor systems. In one case, each sensor receives or does not receive a signal obstructed by noise. In another, each sensor receives data driven by Lévy processes with large or small jumps. In either case, these give rise to four possibilities. Infinitesimal generators are presented and analyzed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. An application of this procedure for stochastic model is also presented in relation to the financial market.

Suggested Citation

  • Michael Roberts & Indranil SenGupta, 2020. "Infinitesimal generators for two-dimensional Lévy process-driven hypothesis testing," Annals of Finance, Springer, vol. 16(1), pages 121-139, March.
    • Handle: RePEc:kap:annfin:v:16:y:2020:i:1:d:10.1007_s10436-019-00355-y
    DOI: 10.1007/s10436-019-00355-y
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    References listed on IDEAS

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    1. Aziz Issaka & Indranil SenGupta, 2017. "Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index," Annals of Finance, Springer, vol. 13(4), pages 401-434, November.
    2. Semere Habtemicael & Indranil SenGupta, 2016. "Pricing variance and volatility swaps for Barndorff-Nielsen and Shephard process driven financial markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-35, December.
    3. Semere Habtemicael & Indranil Sengupta, 2016. "Pricing Covariance Swaps For Barndorff–Nielsen And Shephard Process Driven Financial Markets," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 1-32, September.
    4. Indranil SenGupta & William Nganje & Erik Hanson, 2021. "Refinements of Barndorff-Nielsen and Shephard Model: An Analysis of Crude Oil Price with Machine Learning," Annals of Data Science, Springer, vol. 8(1), pages 39-55, March.
    5. repec:dau:papers:123456789/332 is not listed on IDEAS
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    Cited by:

    1. Michael Roberts & Indranil SenGupta, 2020. "Sequential hypothesis testing in machine learning, and crude oil price jump size detection," Papers 2004.08889, arXiv.org, revised Dec 2020.
    2. Shantanu Awasthi & Indranil SenGupta, 2020. "First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process," Papers 2006.07167, arXiv.org, revised Jan 2021.
    3. Minglian Lin & Indranil SenGupta, 2021. "Analysis of optimal portfolio on finite and small time horizons for a stochastic volatility market model," Papers 2104.06293, arXiv.org.
    4. Minglian Lin & Indranil SenGupta, 2023. "Analysis of optimal portfolio on finite and small-time horizons for a stochastic volatility model with multiple correlated assets," Papers 2302.06778, arXiv.org, revised Dec 2023.
    5. Indranil SenGupta & William Nganje & Erik Hanson, 2021. "Refinements of Barndorff-Nielsen and Shephard Model: An Analysis of Crude Oil Price with Machine Learning," Annals of Data Science, Springer, vol. 8(1), pages 39-55, March.
    6. Humayra Shoshi & Indranil SenGupta, 2020. "Hedging and machine learning driven crude oil data analysis using a refined Barndorff-Nielsen and Shephard model," Papers 2004.14862, arXiv.org, revised Feb 2021.
    7. Shubham Ekapure & Nuruddin Jiruwala & Sohan Patnaik & Indranil SenGupta, 2021. "A data-science-driven short-term analysis of Amazon, Apple, Google, and Microsoft stocks," Papers 2107.14695, arXiv.org.
    8. Xianfei Hui & Baiqing Sun & Indranil SenGupta & Yan Zhou & Hui Jiang, 2022. "Stochastic volatility modeling of high-frequency CSI 300 index and dynamic jump prediction driven by machine learning," Papers 2204.02891, arXiv.org, revised Jan 2023.
    9. Nicholas Salmon & Indranil SenGupta, 2021. "Fractional Barndorff-Nielsen and Shephard model: applications in variance and volatility swaps, and hedging," Annals of Finance, Springer, vol. 17(4), pages 529-558, December.

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    More about this item

    Keywords

    Lévy process; Infinitesimal generator; Hypothesis tests; Viscosity solution; Oil price;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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