arXiv subjects

Ivana Geček Tuđen

Publications and source records attributed to Ivana Geček Tuđen.

2 recordsLinked to original sources

arXiv2017

Ruin probability for discrete risk processes

We study the discrete time risk process modelled by the skip-free random walk and we derive the results connected to the ruin probability, such as crossing the fixed level, for this kind of process. We use the method relying on the classical ballot theorems to derive these results and compare them to the results obtained for the continuous time version of the risk process. We further generalize this model by adding the perturbation and, still relying on the skip-free structure of that process, we generalize the previous results on crossing the fixed level for the generalized discrete time risk process.

math.PR↗

arXiv2017

Distribution of suprema for generalized risk processes

We study a generalized risk process $X(t)=Y(t)-C(t)$, $t\in[0,τ]$, where $Y$ is a Lévy process, $C$ an independent subordinator and $τ$ an independent exponential time. Dropping the standard assumptions on the finite expectations of the processes $Y$ and $C$ and the net profit condition, we derive a Pollaczek-Khinchine type formula for the supremum of the dual process $\widehat{X}=-X$ on $[0,τ]$ which generalizes the results obtained in \cite{HPSV1}. We also discuss which assumptions are necessary for deriving this formula, specially from the point of view of the ladder process.

math.PR↗