We consider the problem of modelling the term structure of defaultable bonds, under minimal assumptions on the default time. In particular, we do not assume the existence of a default intensity and we therefore allow for the possibility of default at predictable times. It turns out that this...

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to...

No-arbitrage surfaces implied from the parameters of benchmark stochastic financial models have attracted considerable attention. They are convenient objects that statically give access to the marginals of the state variables and dynamically to their law. The former help to price vanillas and to...

We consider a continuous time Markov chain on a countable state space. We prove a joint large deviation principle (LDP) of the empirical measure and current in the limit of large time interval. The proof is based on results on the joint large deviations of the empirical measure and flow obtained...

Stochastic filtering is defined as the estimation of a partially observed dynamical system. Approximating the solution of the filtering problem with Gaussian mixtures has been a very popular method since the 1970s. Despite nearly fifty years of development, the existing work is based on the...

For α∈(0,2) and M0, we consider a family of nonlocal operators {Δ+aαΔα/2,a∈(0,M]} on Rd under Kato class gradient perturbation. We establish the existence and uniqueness of their fundamental solutions, and derive their sharp two-sided estimates. The estimates give explicit dependence on...

We study the long time behaviour of the speed of a particle moving in Rd under the influence of a random time-dependent potential representing the particle’s environment. The particle undergoes successive scattering events that we model with a Markov chain for which each step represents a...

We consider a q-TASEP model started from step initial condition where all but finitely many particles have speed 1 and a few particles are slower. It is shown in Ferrari and Veto (2013) that the rescaled particles position of q-TASEP with identical hopping rates obeys a limit theorem à la...

For symmetric random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical eigenvalue distribution can be obtained by analyzing a Gaussian matrix with the same covariance structure. This class contains both...

Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility, which may depend on both the control and the mean field....