On the gamma-reflected processes with fBm input

Abstract

Define a $\gamma$-reflected process $W_{\gamma }(t)=Y_H(t)-\gamma {\inf }_{s\in [0,t]}{Y}_H(s)$, $t\ge 0$ with input process $\{Y_H(t),t\ge 0\}$ which is a fractional Brownian motion with Hurst index $H\in (0,1)$ and a negative linear trend. In risk theory $R_{\gamma }(t)=u-W_{\gamma }(t),t\ge 0$ is referred to as the risk process with tax of a loss-carry-forward type, whereas in queueing theory $W_1$ is referred to as the queue length process. In this paper, we investigate the ruin probability and the ruin time of the risk process $R_{\gamma },\gamma \in [0,1]$ over a surplus dependent time interval $[0,T_u]$.

References in corpus (1)

• Convolution equivalent Lévy processes and first passage times