IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/111021.html
   My bibliography  Save this paper

First hitting time of Brownian motion on simple graph with skew semiaxes

Author

Listed:
  • Dassios, Angelos
  • Zhang, Junyi

Abstract

Consider a stochastic process that lives on n-semiaxes emanating from a common origin. On each semiaxis it behaves as a Brownian motion and at the origin it chooses a semiaxis randomly. In this paper we study the first hitting time of the process. We derive the Laplace transform of the first hitting time, and provide the explicit expressions for its density and distribution functions. Numerical examples are presented to illustrate the application of our results.

Suggested Citation

  • Dassios, Angelos & Zhang, Junyi, 2022. "First hitting time of Brownian motion on simple graph with skew semiaxes," LSE Research Online Documents on Economics 111021, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:111021
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/111021/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Becher, Christopher & Millard, Stephen & SoramÃÂäki, Kimmo, 2008. "The network topology of CHAPS Sterling," Bank of England working papers 355, Bank of England.
    2. Christopher Becher & Marco Galbiati & Merxe Tudela, 2008. "The timing and funding of CHAPS sterling payments," Economic Policy Review, Federal Reserve Bank of New York, vol. 14(Sep), pages 113-133.
    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. Clara Machado & Carlos León & Miguel Sarmiento & Freddy Cepeda & Orlando Chipatecua & Jorge Cely, 2011. "Riesgo Sistémico Y Estabilidad Del Sistema De Pagos De Alto Valor En Colombia: Análisis Bajo," Revista ESPE - Ensayos sobre Política Económica, Banco de la Republica de Colombia, vol. 29(65), pages 106-175, June.
    2. Perlin, Marcelo & Schanz, Jochen, 2011. "System-wide liquidity risk in the United Kingdom’s large-value payment system: an empirical analysis," Bank of England working papers 427, Bank of England.
    3. Langfield, Sam & Liu, Zijun & Ota, Tomohiro, 2014. "Mapping the UK interbank system," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 288-303.
    4. Yoshiharu Maeno & Kenji Nishiguchi & Satoshi Morinaga & Hirokazu Matsushima, 2014. "Impact of credit default swaps on financial contagion," Papers 1411.1356, arXiv.org.
    5. Morten L. Bech & Antoine Martin & James J. McAndrews, 2012. "Settlement liquidity and monetary policy implementation—lessons from the financial crisis," Economic Policy Review, Federal Reserve Bank of New York, vol. 18(Mar), pages 3-20.
    6. Ricardo Mariño-Martínez & Carlos León & Carlos Cadena-Silva, 2020. "Las entidades de contrapartida central en la mitigación del riesgo de contraparte y de liquidez: El caso de los derivados cambiarios en Colombia," Borradores de Economia 1101, Banco de la Republica de Colombia.
    7. Rainone, Edoardo, 2020. "The network nature of over-the-counter interest rates," Journal of Financial Markets, Elsevier, vol. 47(C).
    8. Ladley, Daniel, 2013. "Contagion and risk-sharing on the inter-bank market," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1384-1400.
    9. Merrouche, Ouarda & Schanz, Jochen, 2010. "Banks' intraday liquidity management during operational outages: Theory and evidence from the UK payment system," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 314-323, February.
    10. Krause, Andreas & Giansante, Simone, 2012. "Interbank lending and the spread of bank failures: A network model of systemic risk," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 583-608.
    11. León, C., 2015. "Financial stability from a network perspective," Other publications TiSEM bb2e4e44-e842-45c6-a946-4, Tilburg University, School of Economics and Management.
    12. De Caux, Robert & Brede, Markus & McGroarty, Frank, 2016. "Payment prioritisation and liquidity risk in collateralised interbank payment systems," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 41(C), pages 139-150.
    13. repec:zbw:bofrdp:2013_019 is not listed on IDEAS
    14. Joaquín Bernal R. & Freddy Cepeda L. & Fabio Ortega C, 2011. "Cuantificación de la contribución de las fuentes de liquidez en el Sistema de Pagos de Alto Valor en Colombia: una aproximación preliminar," Borradores de Economia 9197, Banco de la Republica.
    15. Caceres-Santos, Jonnathan & Rodriguez-Martinez, Anahi & Caccioli, Fabio & Martinez-Jaramillo, Serafin, 2020. "Systemic risk and other interdependencies among banks in Bolivia," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 1(1).
    16. Denbee, Edward & Garratt, Rodney & Zimmerman, Peter, 2014. "Variations in liquidity provision in real-time payment systems," Bank of England working papers 513, Bank of England.
    17. Jonnathan Cáceres Santos & René Aldazosa Inchauste, 2013. "Analizando el riesgo sistémico en Bolivia: una aplicación de modelos de topología de redes y simulación al funcionamiento del Sistema de Pagos de Alto Valor," Revista de Análisis del BCB, Banco Central de Bolivia, vol. 17(2(2012)-1), pages 45-80, January.
    18. Blasques, Francisco & Bräuning, Falk & Lelyveld, Iman van, 2018. "A dynamic network model of the unsecured interbank lending market," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 310-342.
    19. Denbee, Edward & Norman, Ben, 2010. "The impact of payment splitting on liquidity requirements in RTGS," Bank of England working papers 404, Bank of England.
    20. Dassios, Angelos & Zhang, Junyi, 2020. "Parisian time of reflected Brownian motion with drift on rays and its application in banking," LSE Research Online Documents on Economics 107495, London School of Economics and Political Science, LSE Library.
    21. Finan, Kevin & Lasaosa, Ana & Sunderland, Jamie, 2013. "Tiering in CHAPS," Bank of England Quarterly Bulletin, Bank of England, vol. 53(4), pages 371-378.

    More about this item

    Keywords

    Brownian motion; simple graph; first hitting time; Inverse Laplace transform; Bromwich integral;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    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:ehl:lserod:111021. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.