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Robustness of Hilbert space-valued stochastic volatility models
Fred Espen Benth, Heidar Eyjolfsson
In this paper we show that Hilbert space-valued stochastic models are robust with respect to perturbation, due to measurement or approximation errors, in the underlying volatility…
Stochastic Integrals and Gelfand Integration in Fréchet Spaces
Fred Espen Benth, Luca Galimberti
We provide a detailed analysis of the Gelfand integral on Fréchet spaces, showing among other things a Vitali theorem, dominated convergence and a Fubini result. Furthermore, the G…
A Topological Proof of Sklar's Theorem in Arbitrary Dimensions
Fred Espen Benth, Giulia Di Nunno, Dennis Schroers
We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.
Sensitivity analysis in the infinite dimensional Heston model
Fred Espen Benth, Giulia Di Nunno, Iben Cathrine Simonsen
We consider the infinite dimensional Heston stochastic volatility model proposed in \arXiv:1706:03500. The price of a forward contract on a non-storable commodity is modelled by a…
Copula Measures and Sklar's Theorem in Arbitrary Dimensions
Fred Espen Benth, Giulia Di Nunno, Dennis Schroers
Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies…
A weak law of large numbers for realised covariation in a Hilbert space setting
Fred Espen Benth, Dennis Schroers, Almut E. D. Veraart
This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an…