Rare and randomly occurring events are important features of the economic world. In continuous time they can easily be modeled by Poisson processes. Analyzing optimal behavior in such a setup requires the appropriate version of the change of variables formula and the Hamilton-Jacobi-Bellman...

We prove some heavy-traffic limit theorems for some nonstationary linear processes which encompass the fractionally differentiated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a non-Gaussian stable distribution. The results are based on an...

This paper studies the optimization of the (<i>S</i>, <i>T</i>) inventory policy, where <i>T</i> is the replenishment interval and <i>S</i> is the order-up-to level. First, we demonstrate that the previously established joint convexity of the long-run average cost is false. Hence, the optimization is not straightforward....

This paper studies likelihood-based estimation and inference in parametric discontinuous threshold regression models with i.i.d. data. The setup allows heteroskedasticity and threshold effects in both mean and variance. By interpreting the threshold point as a “middle” boundary of the...

We study the asset allocation of defined benefit pension plans of the type designed and sponsored by firms with the aim of providing a lifetime pension to the employees at the age of retirement. Benefits are stochastic, combining Poisson jumps with Brownian uncertainty. The sponsor dynamically...

Let ηt be a Poisson point process of intensity t≥1 on some state space Y and let f be a non-negative symmetric function on Yk for some k≥1. Applying f to all k-tuples of distinct points of ηt generates a point process ξt on the positive real half-axis. The scaling limit of ξt as t tends...

Random flights in Rd,d≥2, with Dirichlet-distributed displacements and uniformly distributed orientation are analyzed. The explicit characteristic functions of the position X¯d(t),t0, when the number of changes of direction is fixed are obtained. The probability distributions are derived by...

According to the δ-shock model, the system fails when the time between two consecutive shocks falls below a fixed threshold δ. This model has a potential application in various fields such as inventory, insurance and system reliability. In this paper, we study run-related generalization of...