  We consider a surplus process of drifted fractional Brownian motion with the
Hurst index $H>1/2$, which appears as a functional limit of drifted compound
Poisson risk models with correlated claims, and this is a kind of
representation of a surplus with a long memory. Our interest is to construct
confidence intervals of the ruin probability of the surplus when the volatility
parameter is unknown. We will obtain the derivative of the ruin probability
w.r.t. the volatility parameter via Malliavin calculus, and apply the delta
method to identify the asymptotic distribution of an estimated ruin
probability.
