Measure-valued affine and polynomial diffusions

Christa Cuchiero, Luca Di Persio, Francesco Guida and Sara Svaluto-Ferro

Stochastic Processes and their Applications, 2024, vol. 175, issue C

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.

Keywords: Measure-valued processes; Polynomial and affine diffusions; Dawson–Watanabe type superprocesses; Martingale problem; Maximum principle (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104392

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