We present a class of Lévy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their ...

In this paper the asymptotic behaviour of the maximum likelihood and Bayesian estimators of a delay parameter is studied. The observed process is supposed to be the solution of a linear stochastic differential equation ...

Let X be a real-valued Lévy process under P in its natural filtration. The minimal entropy martingale measure is defined as an absolutely continuous martingale measure that minimizes the relative entropy with respect to ...

We obtain an explicit form of fine large deviation theorems for the log-likelihood ratio in testing models with observed Ornstein-Uhlenbeck processes and get explicit rates of decrease for error probabilities of Neyman-Pearson, ...

We study a bond market model and related term structure of interest rates where prices of zero coupon bonds are driven by a jump-diffusion process. We present a criterion on the deterministic forward rate volatilities under ...

Let (X(t), t ≥ −1) and (Y (t), t ≥ 0) be stochastic processes satisfying dX(t) = aX(t)dt + bX(t − 1)dt + dW(t) and dY (t) = X(t)dt + dV (t), respectively. Here (W(t), t ≥ 0) and (V (t), t ≥ 0) are independent standard ...

Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. ...