Large and moderate deviations for stochastic Volterra systems

Abstract

We provide a unified treatment of pathwise Large and Moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not necessarily of convolution form. Our methodology is based on the weak convergence approach by Budhijara, Dupuis and Ellis. We show in particular how this framework encompasses most rough volatility models used in mathematical finance and generalises many recent results in the literature.

39 pages

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• Large deviations for infinite dimensional stochastic dynamical systems
• Large Deviations and Importance Sampling for Systems of Slow-Fast Motion
• Uniqueness for Volterra-type stochastic integral equations
• Many-Server Asymptotics for Join-the-Shortest-Queue: Large Deviations and Rare Events
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Cited by in corpus (6)

• Time fractional stochastic differential equations driven by pure jump Lévy noise
• Large deviations of slow-fast systems driven by fractional Brownian motion
• Multifractal Fractional Ornstein-Uhlenbeck Processes
• Pathwise large deviations for white noise chaos expansions
• Small-time, large-time and $H\to 0$ asymptotics for the Rough Heston model
• Small-time central limit theorems for stochastic Volterra integral equations and their Markovian lifts