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Brownian Bridges on Random Intervals

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  • Matteo Ludovico Bedini
  • Rainer Buckdahn
  • Hans-Jurgen Engelbert

Abstract

The issue of giving an explicit description of the flow of information concerning the time of bankruptcy of a company (or a state) arriving on the market is tackled by defining a bridge process starting from zero and conditioned to be equal to zero when the default occurs. This enables to catch some empirical facts on the behavior of financial markets: when the bridge process is away from zero, investors can be relatively sure that the default will not happen immediately. However, when the information process is close to zero, market agents should be aware of the risk of an imminent default. In this sense the bridge process leaks information concerning the default before it occurs. The objective of this first paper on Brownian bridges on stochastic intervals is to provide the basic properties of these processes.

Suggested Citation

  • Matteo Ludovico Bedini & Rainer Buckdahn & Hans-Jurgen Engelbert, 2016. "Brownian Bridges on Random Intervals," Papers 1601.01811, arXiv.org.
    • Handle: RePEc:arx:papers:1601.01811
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    References listed on IDEAS

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    1. Monique Jeanblanc & Marc Yor & Marc Chesney, 2010. "Mathematical Methods for Financial Markets," Finance, Presses universitaires de Grenoble, vol. 31(1), pages 81-85.
    2. Jeanblanc, Monique & Le Cam, Yann, 2009. "Progressive enlargement of filtrations with initial times," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2523-2543, August.
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    Cited by:

    1. Matteo Ludovico Bedini & Rainer Buckdahn & Hans-Jurgen Engelbert, 2016. "Unexpected Default in an Information Based Model," Papers 1611.02952, arXiv.org.
    2. Bedini, Matteo L. & Hinz, Michael, 2017. "Credit default prediction and parabolic potential theory," Statistics & Probability Letters, Elsevier, vol. 124(C), pages 121-125.
    3. Juhasz, Peter & Varadi, Kata & Vidovics-Dancs, Agnes & Szaz, Janos, 2017. "Measuring Path Dependency," UTMS Journal of Economics, University of Tourism and Management, Skopje, Macedonia, vol. 8(1), pages 29-37.

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