Gerhold, S., & Wiedermann, K. (2023, March 7). A CLT for Solutions to Stochastic Volterra Integral Equations [Conference Presentation]. 16th German Probability and Statistics Days GPSD 2023, Essen, Germany. http://hdl.handle.net/20.500.12708/191889
E105-01 - Forschungsbereich Risikomanagement in Finanz- und Versicherungsmathematik
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Date (published):
7-Mar-2023
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Event name:
16th German Probability and Statistics Days GPSD 2023
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Event date:
7-Mar-2023 - 10-Mar-2023
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Event place:
Essen, Germany
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Keywords:
Central Limit Theorem; Stochastic Volterra Integral Equation; Riemann-Liouville kernel; Small-Time Asymptotic; Non-Markovianity
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Abstract:
In this work, we prove a central limit theorem for the finite-dimensional distributions of solutions to stochastic Volterra integral equations, where we focus on coefficients satisfying linear growth and Hölder conditions. As we consider the (potentially singular) Riemann-Liouville kernel, the Hurst Parameter H>0 plays an essential role in choosing the appropriate normalizing sequence for the CLT. Provided that the density of the solution is sufficiently smooth, we can, moreover, prove the non-Markovianity of the process, which is of importance for applications in mathematical finance as it significantly complicates pricing and hedging of financial derivatives. Joint work with Stefan Gerhold.
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Research Areas:
Mathematical Methods in Economics: 20% Fundamental Mathematics Research: 80%