IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/43567.html
   My bibliography  Save this paper

On multi-particle Brownian survivals and the spherical Laplacian

Author

Listed:
  • B S, Balakrishna

Abstract

The probability density function for survivals, that is for transitions without hitting the barrier, for a collection of particles driven by correlated Brownian motions is analyzed. The analysis is known to lead one to a study of the spectrum of the Laplacian on domains on the sphere in higher dimensions. The first eigenvalue of the Laplacian governs the large time behavior of the probability density function and the asymptotics of the hitting time distribution. It is found that the solution leads one naturally to a generating function for the eigenvalues and multiplicities of the Laplacian. Analytical properties of the generating function suggest a simple scaling procedure for determining the eigenvalues readily applicable for a homogeneous collection correlated particles. Comparison of the first eigenvalue with the theoretical and numerical results of Ratzkin and Treibergs for some special domains shows remarkable agreement.

Suggested Citation

  • B S, Balakrishna, 2013. "On multi-particle Brownian survivals and the spherical Laplacian," MPRA Paper 43567, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:43567
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/43567/1/MPRA_paper_43567.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/43984/1/MPRA_paper_43984.pdf
    File Function: revised version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/44459/1/MPRA_paper_44459.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhou, Chunsheng, 2001. "An Analysis of Default Correlations and Multiple Defaults," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 555-576.
    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. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    2. Lavrutich, Maria, 2016. "Strategic real options : Entry deterrence and exit inducement," Other publications TiSEM a83e0597-6450-4df7-a1e6-7, Tilburg University, School of Economics and Management.
    3. Mercadier, Mathieu & Lardy, Jean-Pierre, 2019. "Credit spread approximation and improvement using random forest regression," European Journal of Operational Research, Elsevier, vol. 277(1), pages 351-365.
    4. Ulrich Erlenmaier & Hans Gersbach, 2014. "Default Correlations in the Merton Model," Review of Finance, European Finance Association, vol. 18(5), pages 1775-1809.
    5. Chakraborty, Suparna & Allen, Linda, 2007. "Revisiting the Level Playing Field: International Lending Responses to Divergences in Japanese Bank Capital Regulations from the Basel Accord," MPRA Paper 1805, University Library of Munich, Germany.
    6. Chamizo, Álvaro & Fonollosa, Alexandre & Novales, Alfonso, 2019. "Forward-looking asset correlations in the estimation of economic capital," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 61(C), pages 264-288.
    7. Wan†Chien Chiu & Juan Ignacio Peña & Chih†Wei Wang, 2015. "Measuring Systemic Risk: Common Factor Exposures and Tail Dependence Effects," European Financial Management, European Financial Management Association, vol. 21(5), pages 833-866, November.
    8. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    9. Alfred Hamerle & Daniel Rösch, 2003. "Risikofaktoren und Korrelationen für Bonitätsveränderungen," Schmalenbach Journal of Business Research, Springer, vol. 55(3), pages 199-223, May.
    10. Mikael Juselius & Nikola Tarashev, 2022. "When uncertainty decouples expected and unexpected losses," BIS Working Papers 995, Bank for International Settlements.
    11. Albrecht, Peter, 2005. "Kreditrisiken - Modellierung und Management: Ein Überblick," German Risk and Insurance Review (GRIR), University of Cologne, Department of Risk Management and Insurance, vol. 1(2), pages 22-152.
    12. Sheen Liu & Howard Qi & Jian Shi & Yan Alice Xie, 2015. "Inferring Default Correlation from Equity Return Correlation," European Financial Management, European Financial Management Association, vol. 21(2), pages 333-359, March.
    13. Mark B. Wise & Vineer Bhansali, 2002. "Implications of Correlated Default For Portfolio Allocation To Corporate Bonds," Papers nlin/0209010, arXiv.org.
    14. Sabine Karl & Tom Fischer, 2013. "Cross-Ownership as a Structural Explanation for Over- and Underestimation of Default Probability," Papers 1301.6069, arXiv.org.
    15. Alexander Lipton & Ioana Savescu, 2012. "A structural approach to pricing credit default swaps with credit and debt value adjustments," Papers 1206.3104, arXiv.org.
    16. Ming Xi Huang, 2010. "Modelling Default Correlations in a Two-Firm Model with Dynamic Leverage Ratios," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2010, March.
    17. Jin Liang & Jun Ma & Tao Wang & Qin Ji, 2011. "Valuation of Portfolio Credit Derivatives with Default Intensities Using the Vasicek Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(1), pages 33-54, March.
    18. Patras, Frédéric, 2006. "A reflection principle for correlated defaults," Stochastic Processes and their Applications, Elsevier, vol. 116(4), pages 690-698, April.
    19. Jan Mutl & Leopold Sögner, 2019. "Parameter estimation and inference with spatial lags and cointegration," Econometric Reviews, Taylor & Francis Journals, vol. 38(6), pages 597-635, July.
    20. Peter Christoffersen & Kris Jacobs & Xisong Jin & Hugues Langlois, 2018. "Dynamic Dependence and Diversification in Corporate Credit [Asymmetric correlations of equity portfolios]," Review of Finance, European Finance Association, vol. 22(2), pages 521-560.

    More about this item

    Keywords

    Brownian; Survival Probability; Hitting Time; Correlation; Laplacian; Spherical Domain; Eigenvalue;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:pra:mprapa:43567. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.