On average losses in the ruin problem with fractional Brownian motion as input (Q626279)

The financial-actuarial risk process is considered with the total claim amount process modelled by a fractional Brownian motion with Hurst parameter \(H\), \(0<H<1\). The authors investigate the average loss \(L\) given ruin in the case where the initial capital \(u\) and the time horizon \(T\) tend to infinity; e.g., for a long time horizon, where \[ \lim\inf_{u\to\infty}{T-uH/(c(1-H))\over u^H\log(u)}>0 \] (\(c\) being the premium income rate), \[ L\sim{2H^{2H}u^{2H-1}\over c^{2H}(1-H)^{2H-1}} \] is the asymptotics of the loss.