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arXiv · 1509.08272

Representation and approximation of ambit fields in Hilbert space

Fred Espen Benth·Heidar Eyjolfsson
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Abstract

We lift ambit fields as introduced by Barndorff-Nielsen and Schmiegel to a class of Hilbert space-valued volatility modulated Volterra processes. We name this class Hambit fields, and show that they can be expressed as a countable sum of weighted real-valued volatility modulated Volterra processes. Moreover, Hambit fields can be interpreted as the boundary of the mild solution of a certain first order stochastic partial differential equation. This stochastic partial differential equation is formulated on a suitable Hilbert space of functions on the positive real line with values in the state space of the Hambit field. We provide an explicit construction of such a space. Finally, we apply this interpretation of Hambit fields to develop a finite difference scheme, for which we prove convergence under some Lipschitz conditions.

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Fred Espen Benth, Heidar Eyjolfsson. 2015-09-28. Representation and approximation of ambit fields in Hilbert space. https://arxiv.org/abs/1509.08272

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