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Ruin probability in a risk model with variable premium intensity and risky investments

Mishura Y., Perestyuk M., Ragulina O.

Opuscula Mathematica

2015

Vol. 35, no. 3

333--352

We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion. We get an exponential bound for the infinite-horizon ruin probability. To this end, we allow the surplus process to explode and investigate the question concerning the probability of explosion of the surplus process between claim arrivals.

Asymptotics of the supremum of scaled Brownian motion

Dębicki K.

Probability and Mathematical Statistics

2001

Vol. 21, Fasc. 1

199--212

We consider the problem of estimating the tail of the distribution of the supremum of scaled Brownian motion B(ƒ(t)) processes with linear drift.Using the local time technique we obtain asymptotics and bounds of Pt≥t0(sup(B(ƒ(t))−t)> u), which are expressed in terms of the expected value of thelocal timeof B(ƒ(t))−tprocesses at levelu.As an application we obtain upper bounds for the tail of distribution of the supremum for some Gaussian processes with stationary increments.