We consider de Finetti's stochastic control problem when the (controlled) process is allowed to spend time under the critical level. More precisely, we consider a generalized version of this control problem in a spectrally negative Lévy model with exponential Parisian ruin. We show that, under...

We consider de Finetti’s stochastic control problem when the (controlled) process is allowed to spend time under the critical level. More precisely, we consider a generalized version of this control problem in a spectrally negative Lévy model with exponential Parisian ruin. We show that,...

Traditionally, Parisian ruin is said to occur when the insurer's surplus process has stayed below level zero continuously for a certain grace period. Inspired by this concept, in this paper we propose a modification by assuming that once a grace period has been granted when the surplus becomes...

Using a Poisson approach, we find Laplace transforms of joint occupation times over n disjoint intervals for spectrally negative Lévy processes. They generalize previous results for dimension two.

We study a mixed hitting-time (MHT) model that specifies durations as the first time a Lévy process— a continuous-time process with stationary and independent increments— crosses a heterogeneous threshold. Such models are of substantial interest because they can be reduced from...

We suggest moment estimators for the parameters of a continuous time GARCH(1,1) process based on equally spaced observations. Using the fact that the increments of the COGARCH(1,1) process are ergodic, the resulting estimators are consistent. We investigate the quality of our estimators in a...

The literature on capital allocation is biased towards an asset modeling framework rather than an actuarial framework. The asset modeling framework leads to the proliferation of inappropriate assumptions about the effect of insurance line of business growth on aggregate loss distributions. This...

We study the relation between Lévy processes under nonlinear expectations, nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one relation between nonlinear Lévy processes and nonlinear Markovian convolution semigroups. Second, we provide a condition on a family of...