IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2009.08010.html
   My bibliography  Save this paper

Tail behavior of stopped L\'evy processes with Markov modulation

Author

Listed:
  • Brendan K. Beare
  • Won-Ki Seo
  • Alexis Akira Toda

Abstract

This article concerns the tail probabilities of a light-tailed Markov-modulated L\'evy process stopped at a state-dependent Poisson rate. The tails are shown to decay exponentially at rates given by the unique positive and negative roots of the spectral abscissa of a certain matrix-valued function. We illustrate the use of our results with an application to the stationary distribution of wealth in a simple economic model in which agents with constant absolute risk aversion are subject to random mortality and income fluctuation.

Suggested Citation

  • Brendan K. Beare & Won-Ki Seo & Alexis Akira Toda, 2020. "Tail behavior of stopped L\'evy processes with Markov modulation," Papers 2009.08010, arXiv.org.
    • Handle: RePEc:arx:papers:2009.08010
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2009.08010
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    2. Benhabib, Jess & Bisin, Alberto & Zhu, Shenghao, 2016. "The Distribution Of Wealth In The Blanchard–Yaari Model," Macroeconomic Dynamics, Cambridge University Press, vol. 20(2), pages 466-481, March.
    3. Costas Arkolakis, 2016. "A Unified Theory of Firm Selection and Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(1), pages 89-155.
    4. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    5. Neng Wang, 2003. "Caballero Meets Bewley: The Permanent-Income Hypothesis in General Equilibrium," American Economic Review, American Economic Association, vol. 93(3), pages 927-936, June.
    6. Alexis Akira Toda & Kieran Walsh, 2015. "The Double Power Law in Consumption and Implications for Testing Euler Equations," Journal of Political Economy, University of Chicago Press, vol. 123(5), pages 1177-1200.
    7. Albornoz, Facundo & Fanelli, Sebastián & Hallak, Juan Carlos, 2016. "Survival in export markets," Journal of International Economics, Elsevier, vol. 102(C), pages 262-281.
    8. Dan Cao & Wenlan Luo, 2017. "Persistent Heterogeneous Returns and Top End Wealth Inequality," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 26, pages 301-326, October.
    9. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.
    10. Kasa, Kenneth & Lei, Xiaowen, 2018. "Risk, uncertainty, and the dynamics of inequality," Journal of Monetary Economics, Elsevier, vol. 94(C), pages 60-78.
    11. Stachurski, John & Toda, Alexis Akira, 2019. "An impossibility theorem for wealth in heterogeneous-agent models with limited heterogeneity," Journal of Economic Theory, Elsevier, vol. 182(C), pages 1-24.
    12. Charles I. Jones & Jihee Kim, 2018. "A Schumpeterian Model of Top Income Inequality," Journal of Political Economy, University of Chicago Press, vol. 126(5), pages 1785-1826.
    13. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    14. Toda, Alexis Akira, 2014. "Incomplete market dynamics and cross-sectional distributions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 310-348.
    15. Shuhei Aoki & Makoto Nirei, 2017. "Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the United States," American Economic Journal: Macroeconomics, American Economic Association, vol. 9(3), pages 36-71, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    2. Gouin-Bonenfant, Emilien & Toda, Alexis Akira, 2018. "Pareto Extrapolation: Bridging Theoretical and Quantitative Models of Wealth Inequality," University of California at San Diego, Economics Working Paper Series qt90n2h2bb, Department of Economics, UC San Diego.
    3. Stachurski, John & Toda, Alexis Akira, 2019. "An impossibility theorem for wealth in heterogeneous-agent models with limited heterogeneity," Journal of Economic Theory, Elsevier, vol. 182(C), pages 1-24.
    4. Émilien Gouin‐Bonenfant & Alexis Akira Toda, 2023. "Pareto extrapolation: An analytical framework for studying tail inequality," Quantitative Economics, Econometric Society, vol. 14(1), pages 201-233, January.
    5. Beare, Brendan K & Toda, Alexis Akira, 2020. "On the emergence of a power law in the distribution of COVID-19 cases," University of California at San Diego, Economics Working Paper Series qt9k5027d0, Department of Economics, UC San Diego.
    6. Lei, Xiaowen, 2019. "Information and Inequality," Journal of Economic Theory, Elsevier, vol. 184(C).
    7. Matthias Birkner & Niklas Scheuer & Klaus Wälde, 2023. "The dynamics of Pareto distributed wealth in a small open economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 607-644, August.
    8. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2020. "The income fluctuation problem and the evolution of wealth," Journal of Economic Theory, Elsevier, vol. 187(C).
    9. Brendan K. Beare & Alexis Akira Toda, 2022. "Determination of Pareto Exponents in Economic Models Driven by Markov Multiplicative Processes," Econometrica, Econometric Society, vol. 90(4), pages 1811-1833, July.
    10. Miyoshi, Yoshiyuki & Toda, Alexis Akira, 2017. "Growth effects of annuities and government transfers in perpetual youth models," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 1-6.
    11. Shuhei Aoki & Makoto Nirei, 2014. "Zipf's Law, Pareto's Law, and the Evolution of Top Incomes in the U.S," Working Papers e074, Tokyo Center for Economic Research.
    12. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.
    13. Tetsugen HARUYAMA, 2021. "A Schumpeterian Exploration of Gini and Top/Bottom Income Shares," Discussion Papers 2125, Graduate School of Economics, Kobe University.
    14. Ji Hyung Lee & Yuya Sasaki & Alexis Akira Toda & Yulong Wang, 2021. "Fixed-k Tail Regression: New Evidence on Tax and Wealth Inequality from Forbes 400," Papers 2105.10007, arXiv.org, revised Sep 2022.
    15. Keiichi Kishi, 2016. "Technology Diffusion, Pareto Distribution, and Patent Policy," Discussion Papers in Economics and Business 16-31, Osaka University, Graduate School of Economics.
    16. Toda, Alexis Akira, 2017. "A Note On The Size Distribution Of Consumption: More Double Pareto Than Lognormal," Macroeconomic Dynamics, Cambridge University Press, vol. 21(6), pages 1508-1518, September.
    17. Kasa, Kenneth & Lei, Xiaowen, 2018. "Risk, uncertainty, and the dynamics of inequality," Journal of Monetary Economics, Elsevier, vol. 94(C), pages 60-78.
    18. Alexis Akira Toda & Kieran James Walsh, 2017. "Fat tails and spurious estimation of consumption‐based asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1156-1177, September.
    19. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
    20. Harmenberg, Karl, 2020. "A Simple Theory of Pareto Earnings," Working Papers 21-2020, Copenhagen Business School, Department of Economics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2009.08010. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.