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Stochastic processes governed by Markovian processes
[Processus stochastiques à incréments Markoviens]

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  • Lee Dinetan

    (GREMAQ - Groupe de recherche en économie mathématique et quantitative - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

Abstract

We introduce a new class of processes aiming at modelling random fluctuations of an asset value more efficiently than traditional Lévy processes. In this study, we consider that the object value C is a real discrete random process (N → R), whose increments are subject to the present state of a "market", described by a Markovian process M : as the successive market states are not pairwise independent, C's fluctuations are not independent either, so C cannot be assimilated as a Lévy process. We call this structure a C-process : we present methods to analyze it, mainly extending the notion of Lundberg's parameter of a diffusion Lévy process, to take M into account during the computations. Once done, we aim more specifically at controlling C's default time T0 = min ({t ∈ N|C(t)

Suggested Citation

  • Lee Dinetan, 2014. "Stochastic processes governed by Markovian processes [Processus stochastiques à incréments Markoviens]," Working Papers hal-01103025, HAL.
    • Handle: RePEc:hal:wpaper:hal-01103025
    Note: View the original document on HAL open archive server: https://hal.science/hal-01103025v1
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    References listed on IDEAS

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    Keywords

    Markovian; ruin; default; risk theory; process;
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