Large and moderate deviations for stochastic Volterra systems

• Published in: Stochastic processes and their applications Vol. 149; pp. 142 - 187
• Main Authors: Jacquier, Antoine, Pannier, Alexandre
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2022; Elsevier
• Subjects: Large deviations; Mathematics; Moderate deviations; Rough volatility; Stochastic Volterra equations; Weak convergence; Weak convergence; 60G22; 60F10; 91G20; Moderate deviations; Large deviations; Stochastic Volterra equations; Rough volatility; rough volatility; large deviations; stochastic Volterra equations; April 15 2022. 2010 Mathematics Subject Classification. 60F10 60G22 91G20 stochastic Volterra equations large deviations moderate deviations weak convergence rough volatility; weak convergence; moderate deviations
• ISSN: 0304-4149; 1879-209X; 1879-209X
• DOI: 10.1016/j.spa.2022.03.017

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 Budhiraja and Dupuis (2019); Dupuis and Ellis (1997). We show in particular how this framework encompasses most rough volatility models used in mathematical finance, yields pathwise moderate deviations for the first time and generalises many recent results in the literature.