Wiedermann, K. (2023, May 25). A CLT for Solutions to SVIEs and Their Non-Markovianity [Presentation]. Workshop: “Volatility is rough. Now what?” 2023, United Kingdom of Great Britain and Northern Ireland (the).
E105-01 - Forschungsbereich Risikomanagement in Finanz- und Versicherungsmathematik
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Date (published):
25-May-2023
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Event name:
Workshop: "Volatility is rough. Now what?" 2023
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Event date:
22-May-2023 - 26-May-2023
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Event place:
United Kingdom of Great Britain and Northern Ireland (the)
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Keywords:
Stochastic Volterra Integral Equation; Central Limit Theorem; Small-Time Asymptotic; Riemann-Liouville kernel; 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%
