Estimation of the Characteristics of the Jumps of a General Poisson-Diffusion Model

Rivista nelle classi B e B per il GEV Area 13 della VQR 2004-2010 : We consider a filtered probability space with a standard Brownian motion W, a simple Poisson process N with constant intensity lambda > 0, and we consider the process Y such that Y_0 in R and _t=a_t dt + sigma_t dW_t + gamma_t dN_t; t>0; (1) a, sigma are predictable bounded stochastic processes, and gamma is a predictable process which is bounded away from zero. A discrete record of n+1 observations {Y_0, Yt_1, . . ., Y_{tₙ₋₁}, Yt_n } is available, with t_i=ih. Using such observations, we construct estimators of Nt_i, i=1, . . ., n, lambda and gtau_j, where tau_j are the instants of jump within [0, nh]. They are consistent and controlled when the number of observations increases and the step h tends to zero.