We introduce a new aspect of a risk process, which is a macro approximation of the flow of a risk reserve. We assume that the underlying process consists of a Brownian motion plus negative jumps, and that the process is observed at discrete time points. In our context, each jump size of the...

We consider semimartingales with jumps that have finite Lvy measures. The purpose of this article is to estimate integral-type functionals of the Lvy measures from discrete observations. We propose two types of estimators: kernel-type and empirical-type estimators, both of which are obtained by...

We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of...

Given discrete samples from Ornstein-Uhlenbeck processes, we consider two kinds of approximated MLE's for the drift parameter, which are asymptotically efficient in ergodic case. Our interest is the rate of convergence of those estimators when the process is non-recurrent. We add a remark when...

We study the first-passage time over a fixed threshold for a pure-jump subordinator with negative drift. We obtain a closed-form formula for its survival function in terms of marginal density functions of the subordinator. We then use this formula to calculate finite-time survival probabilities...

The Markov additive process (MAP) has become an increasingly popular modeling tool in the applied probability literature. In many applications, quantities of interest are represented as functionals of MAPs and potential measures, also known as resolvent measures, have played a key role in the...