arXiv subjects

Przemysław Światek

Publications and source records attributed to Przemysław Światek.

2 recordsLinked to original sources

arXiv2017

Discrete time ruin probability with Parisian delay

In this paper we evaluate the probability of the discrete time Parisian ruin that occurs when surplus process stays below or at zero at least for some fixed duration of time $d>0$. We identify expressions for the ruin probabilities within finite and infinite-time horizon. We also find their light and heavy-tailed asymptotics when initial reserves approach infinity. Finally, we calculate these probabilities for a few explicit examples.

math.PR↗

arXiv2011

Loss rate for a general Lévy process with downward periodic barrier

In this paper we consider a general Lévy process $X$ reflected at downward periodic barrier $A_t$ and constant upper barrier $K$ giving a process $V^K_t=X_t+L^A_t-L^K_t$. We find the expression for a loss rate defined by $l^K=\mathbb{E} L^K_1$ and identify its asymptotics as $K\to\infty$ when $X$ has light-tailed jumps and $\mathbb{E}X_1<0$.

math.PR↗