We study the problem of estimating the coefficients of a diffusion (Xl, t 2:: 0); the estimation is based on discrete data Xn . . n = 0, 1, ... ,N. The sampling frequency delta t is constant , and asymptotics arc taken at the number of observations tends to infinity. We prove that the problem of...

We introduce and analyse numerical methods for the treatment of inverse problems, based on an adaptive wavelet Galerkin discretization. These methods combine the theoretical advantages of the wavelet-vaguelette decomposition (WVD) in terms of optimally adapting to the unknown smoothness of the...

Stochastic Volatility (SV) models are widely used in financial applications. To decide whether standard parametric restrictions are justified for a given dataset, a statistical test is required. In this paper, we develop such a test based on the linear state space representation. We provide a...

We study nonparametric estimation of the volatility function of a diffusion process from discrete data, when the data are blurred by additional noise. This noise can be white or correlated, and serves as a model for microstructure effects in financial modeling, when the data are given on an...

We study the problem of estimating the time dependent diffusion coefficient of a diffusion process in a nonparametric setting, when the sample path is observed at discrete times. We look at global Lp-error loss over a wide range of function spaces (namely, Besov spaces). We exhibit the minimax...

We estimate the mean function and the conditional variance (the volatility function) of a nonlinear first-order autoregressive model nonparametrically. Minimax rates of convergence are established over a scale of Besov bodies Bspq and a range of global Lp' error measurements, for...

We consider the following hidden Markov chain problem: estimate the finite-dimensional parameter [theta] in the equation when we observe discrete data Xi/n at times i=0,...,n from the diffusion . The processes (Wt)t[set membership, variant][0,1] and (Bt)t[set membership, variant][0,1] are two...

We study the nonparametric estimation of the coefficients of a 1-dimensional diffusion process from discrete observations. Different asymptotic frameworks are considered. Minimax rates of convergence are studied over a wide range of Besov smoothness classes. We construct estimators based on...

In a complete market with a constant interest rate and a risky asset, which is a linear diffusion process, we are interested in the discrete time hedging of a European vanilla option with payoff function f. As regards the perfect continuous hedging, this discrete time strategy induces, for the...