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Pré-Publication, Document De Travail Année : 2024

Feller's test for explosions of stochastic Volterra equations

Résumé

This paper provides a Feller’s test for explosions of one-dimensional continuous stochastic Volterra processes of convolution type. The study focuses on dynamics governed by nonsingular kernels, which preserve the semimartingale property of the processes and introduce memory features through a path- dependent drift. In contrast to the classical path-independent case, the sufficient condition derived in this study for a Volterra process to remain in the interior of an interval is generally more restrictive than the necessary condition. The results are illustrated with three specifications of the dynamics: the Volterra square-root diffusion, the Volterra Jacobi process and the Volterra power-type diffusion. For the Volterra square-root diffusion, also known as the Volterra CIR process, the paper presents a detailed discussion on the approximation of the singular fractional kernel with a sum of exponentials, a method commonly employed in the mathematical finance literature.
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hal-04617550 , version 1 (19-06-2024)

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  • HAL Id : hal-04617550 , version 1

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Alessandro Bondi, Sergio Pulido. Feller's test for explosions of stochastic Volterra equations. 2024. ⟨hal-04617550⟩
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