IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v174y2024ics0304414924000887.html

On moments of integrals with respect to Markov additive processes and of Markov modulated generalized Ornstein–Uhlenbeck processes

Author

Listed:
  • Behme, Anita
  • Di Tella, Paolo
  • Sideris, Apostolos

Abstract

We establish sufficient conditions for the existence, and derive explicit formulas for the κ’th moments, κ≥1, of Markov modulated generalized Ornstein–Uhlenbeck processes as well as their stationary distributions. In particular, the running mean, the autocovariance function, and integer moments of the stationary distribution are derived in terms of the characteristics of the driving Markov additive process.

Suggested Citation

  • Behme, Anita & Di Tella, Paolo & Sideris, Apostolos, 2024. "On moments of integrals with respect to Markov additive processes and of Markov modulated generalized Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:spapps:v:174:y:2024:i:c:s0304414924000887
    DOI: 10.1016/j.spa.2024.104382
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924000887
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2024.104382?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Lindner, Alexander & Maller, Ross, 2005. "Lévy integrals and the stationarity of generalised Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 115(10), pages 1701-1722, October.
    2. Zhang, Lidong & Jiang, Chunmei, 2009. "Stationary distribution of reflected O-U process with two-sided barriers," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 177-181, January.
    3. Kevei, Péter, 2018. "Ergodic properties of generalized Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 156-181.
    4. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    5. P. Salminen & L. Vostrikova, 2016. "On exponential functionals of processes with independent increments," Papers 1610.08732, arXiv.org, revised Mar 2018.
    6. Paulsen, Jostein, 1993. "Risk theory in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 327-361, June.
    7. Søren Asmussen & Mogens Bladt, 2022. "Gram–Charlier methods, regime-switching and stochastic volatility in exponential Lévy models," Quantitative Finance, Taylor & Francis Journals, vol. 22(4), pages 675-689, April.
    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. Behme, Anita & Lindner, Alexander & Reker, Jana & Rivero, Victor, 2021. "Continuity properties and the support of killed exponential functionals," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 115-146.
    2. Kostadinova, Radostina, 2007. "Optimal investment for insurers when the stock price follows an exponential Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 250-263, September.
    3. Anita Behme, 2024. "Volatility modeling in a Markovian environment: Two Ornstein-Uhlenbeck-related approaches," Papers 2407.05866, arXiv.org.
    4. Valentin Courgeau & Almut E. D. Veraart, 2022. "Likelihood theory for the graph Ornstein-Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 227-260, July.
    5. Behme, Anita & Chong, Carsten & Klüppelberg, Claudia, 2015. "Superposition of COGARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1426-1469.
    6. Klüppelberg, Claudia & Kostadinova, Radostina, 2008. "Integrated insurance risk models with exponential Lévy investment," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 560-577, April.
    7. Bertoin, Jean, 2019. "Ergodic aspects of some Ornstein–Uhlenbeck type processes related to Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1443-1454.
    8. Behme, Anita & Lindner, Alexander, 2012. "Multivariate generalized Ornstein–Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1487-1518.
    9. Thomas Gkelsinis & Alex Karagrigoriou, 2020. "Theoretical Aspects on Measures of Directed Information with Simulations," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    10. Madan, Dilip B. & Wang, King, 2021. "The structure of financial returns," Finance Research Letters, Elsevier, vol. 40(C).
    11. Long, Hongwei & Ma, Chunhua & Shimizu, Yasutaka, 2017. "Least squares estimators for stochastic differential equations driven by small Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1475-1495.
    12. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
    13. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    14. Vladimir Tsenkov, 2009. "Financial Markets Modelling," Economic Thought journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 5, pages 87-96.
    15. Yuri Kabanov & Platon Promyslov, 2023. "Ruin probabilities for a Sparre Andersen model with investments: the case of annuity payments," Finance and Stochastics, Springer, vol. 27(4), pages 887-902, October.
    16. Fred Espen Benth & Martin Groth & Rodwell Kufakunesu, 2007. "Valuing Volatility and Variance Swaps for a Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(4), pages 347-363.
    17. Torben G. ANDERSEN & Tim BOLLERSLEV & Nour MEDDAHI, 2002. "Correcting The Errors : A Note On Volatility Forecast Evaluation Based On High-Frequency Data And Realized Volatilities," Cahiers de recherche 21-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    18. Audrino, Francesco & Corsi, Fulvio, 2010. "Modeling tick-by-tick realized correlations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2372-2382, November.
    19. Julie Lyng Forman & Michael Sørensen, 2008. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 438-465, September.
    20. Gonzalez, Jhonny & Moriarty, John & Palczewski, Jan, 2017. "Bayesian calibration and number of jump components in electricity spot price models," Energy Economics, Elsevier, vol. 65(C), pages 375-388.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    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:eee:spapps:v:174:y:2024:i:c:s0304414924000887. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.