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Uniform Integrability of a Single Jump Local Martingale with State-Dependent Characteristics

Author

Listed:
  • Michael Schatz

    (ETH Zurich)

  • Didier Sornette

    (ETH Zürich and Swiss Finance Institute)

Abstract
We investigate a deterministic criterion to determine whether a diffusive local martingale with a single jump and state-dependent characteristics is a uniformly integrable martingale. We allow the diffusion coefficient, the jump hazard rate and the relative jump size to depend on the state and prove that the process is a uniformly integrable martingale if and only if the relative jump size is bounded away from one and the hazard rate is large enough compared to the diffusion component. The result helps to classify seemingly explosive behaviour in diffusive local martingales compensated by the existence of a jump. Moreover, processes of this type can be used to model financial bubbles in stock prices as deviation from the fundamental value. We present a simple framework to illustrate this application.

Suggested Citation

  • Michael Schatz & Didier Sornette, 2017. "Uniform Integrability of a Single Jump Local Martingale with State-Dependent Characteristics," Swiss Finance Institute Research Paper Series 17-21, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1721
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Uniformly Integrable Martingales; Local Martingales; Single Jump; Explosive Diffusion Processes; Financial Bubbles;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G01 - Financial Economics - - General - - - Financial Crises
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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