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The [phi]-Martingale

Author

Listed:
  • Vrins, F.

    (Université catholique de Louvain, CORE, Belgium)

  • Jeanblanc, M.

    (Université d’Evry Val d’Essonne)

Abstract

In this paper we focus on continuous martingales evolving in the unit interval [0,1]. We first review some results about the martingale property of solution to one-dimensional driftless stochastic differential equations. We then provide a simple way to construct and handle such processes. One of these martingales proves to be analytically tractable, and received the specific name of [phi]-martingale. It is shown that up to shifting and rescaling constants, it is the only martingale (with the trivial constant, Brownian motion and Geometric Brownian motion) having a separable coefficient (t, x) = g(t)h(x) that can be obtained via a time-homogeneous mapping of Gaussian processes. The approach is applied to the modeling of stochastic survival probabilities.

Suggested Citation

  • Vrins, F. & Jeanblanc, M., 2015. "The [phi]-Martingale," LIDAM Discussion Papers CORE 2015022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2015022
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2015.html
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    References listed on IDEAS

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    10. NESTEROV, Yurii, 2015. "Complexity bounds for primal-dual methods minimizing the model of objective function," LIDAM Discussion Papers CORE 2015003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Citations

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    Cited by:

    1. Frédéric Vrins, 2017. "Wrong-Way Risk Cva Models With Analytical Epe Profiles Under Gaussian Exposure Dynamics," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-35, November.
    2. Cheikh Mbaye & Fr'ed'eric Vrins, 2019. "An arbitrage-free conic martingale model with application to credit risk," Papers 1909.02474, arXiv.org.

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    More about this item

    Keywords

    continuous stochastic processes; Gaussian processes; bounded martingales; local martingales; Azema supermartingale; credit risk modeling;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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