Abstract Let {T 1, Y 1}∞ i= 1 be a sequence of positive independent random variables. Let,
also, Z 1= βY′ 1− πT i, i= 1, 2,…, where Y′ 1= Max (0, Y i− w), w⩾ 0, and where β< 0 and …

Some classical results of ruin theory are derived by probabilistic methods, which have an
interest of their own. Let X 1, X 2,… be positive, independent and identically distributed …

We generalize some results of Gerber concerned with the probability of ruin in a linear
model. In particular, we remove the boundedness restriction for the underlying distribution …

We obtain lower and upper bounds for the severity of ruin in the renewal (Sparre Andersen)
model of risk theory. We present two types of bounds:(i) bounds applicable generally; and …

We consider quantities such as the probability that a two-dimensional random walk crosses
the ordinate y for the first time to the left of the abscissa x, and describe the asymptotic …

This paper studies the Parisian ruin problem first proposed by Dassios and Wu (2008a, b),
where the Parisian ruin time is defined to be the first time when the surplus process has …

In this paper, we mainly consider the uniform asymptotic behavior for the finitetime ruin
probabilities of a two-dimensional insurance model. In this model, the insurance company …

Let {Zn} n≥ 0 be a random walk with a negative drift and independent and identically
distributed increments with heavy-tailed distribution, and let M= supn≥ 0Zn be its …

A defective renewal equation is derived for the expected discounted penalty due at
ruin,[Formula: see text] in a risk model with Erlang (n) claim inter-arrival times. The approach …

In this paper the author shows how methods which have been applied to derive results for
the classical risk process can be adapted to derive results for a class of risk processes …