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Measure-valued affine and polynomial diffusions

Author

Listed:
  • Cuchiero, Christa
  • Di Persio, Luca
  • Guida, Francesco
  • Svaluto-Ferro, Sara

Abstract

We introduce a class of measure-valued processes, which – in analogy to their finite dimensional counterparts – will be called measure-valued polynomial diffusions. We show the so-called moment formula, i.e. a representation of the conditional marginal moments via a system of finite dimensional linear PDEs. Furthermore, we characterize the corresponding infinitesimal generators obtaining a representation analogous to polynomial diffusions on R+m, in cases where their domain is large enough. In general the infinite dimensional setting allows for richer specifications strictly beyond this representation. As a special case, we recover measure-valued affine diffusions, sometimes also called Dawson–Watanabe superprocesses. From a mathematical finance point of view, the polynomial framework is especially attractive since it allows to transfer many famous finite dimensional models and their tractability properties to an infinite dimensional measure-valued setting.

Suggested Citation

  • Cuchiero, Christa & Di Persio, Luca & Guida, Francesco & Svaluto-Ferro, Sara, 2024. "Measure-valued affine and polynomial diffusions," Stochastic Processes and their Applications, Elsevier, vol. 175(C).
    • Handle: RePEc:eee:spapps:v:175:y:2024:i:c:s030441492400098x
    DOI: 10.1016/j.spa.2024.104392
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    References listed on IDEAS

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