Large deviations for Poisson random measures and processes with independent increments

Large deviation principle for a mixed fractional and jump diffusion process

We study the asymptotic behavior of a solution of a mixed differential equation driven by independent fractional Brownian motion with Hurst index H ∈ ( 0 ; 1 ) {H\in(0;1)} and compensated Poisson process. This study consists in determining the uniform Freidlin–Wentzell estimates in a temporal distribution space.

Long-Time Trajectorial Large Deviations and Importance Sampling for Affine Stochastic Volatility Models

We establish a pathwise large deviation principle for affine stochastic volatility models introduced by Keller-Ressel (2011), and present an application to variance reduction for Monte Carlo computation of prices of path-dependent options in these models, extending the method developed by Genin and Tankov (2020) for exponential Lévy models. To this end, we apply an exponentially affine change of measure and use Varadhan’s lemma, in the fashion of Guasoni and Robertson (2008) and Robertson (2010), to approximate the problem of finding the measure that minimizes the variance of the Monte Carlo estimator. We test the method on the Heston model with and without jumps to demonstrate its numerical efficiency.

The Kramers problem for SDEs driven by small, accelerated Lévy noise with exponentially light jumps

We establish Freidlin–Wentzell results for a nonlinear ordinary differential equation starting close to the stable state [Formula: see text], say, subject to a perturbation by a stochastic integral which is driven by an [Formula: see text]-small and [Formula: see text]-accelerated Lévy process with exponentially light jumps. For this purpose, we derive a large deviations principle for the stochastically perturbed system using the weak convergence approach developed by Budhiraja, Dupuis, Maroulas and collaborators in recent years. In the sequel, we solve the associated asymptotic first escape problem from the bounded neighborhood of [Formula: see text] in the limit as [Formula: see text] which is also known as the Kramers problem in the literature.