We study the tail asymptotics of the r.v. X(T) where {X(t)} is a stochastic process with a linear drift and satisfying some regularity conditions like a central limit theorem and a large deviations principle, and T is an independent r.v. with a subexponential distribution. We find that the tail...

For a random walk with negative mean and heavy-tailed increment distribution F, it is well known that under suitable subexponential assumptions, the distribution [pi] of the maximum has a tail [pi](x,[infinity]) which is asymptotically proportional to . We supplement here this by a local result...

Let [psi]i(u) be the probability of ruin for a risk process which has initial reserve u and evolves in a finite Markovian environment E with initial state i. Then the arrival intensity is [beta]j and the claim size distribution is Bj when the environment is in state j[set membership, variant]E....

We consider a model of a financial corporation which has to find an optimal policy balancing its risk and expected profits. The example treated in this paper is related to an insurance company with the risk control method known in the industry as excess-of-loss reinsurance. Under this scheme the...

In a bonus-malus system in car insurance, the bonus class of a customer is updated from one year to the next as a function of the current class and the number of claims in the year (assumed Poisson). Thus the sequence of classes of a customer in consecutive years forms a Markov chain, and most...

Consider the American put and Russian option (Ann. Appl. Probab. 3 (1993) 603; Theory Probab. Appl. 39 (1994) 103; Ann. Appl. Probab. 3 (1993) 641) with the stock price modeled as an exponential Lévy process. We find an explicit expression for the price in the dense class of Lévy processes with...

Let (Y1,...,Yn) have a joint n-dimensional Gaussian distribution with a general mean vector and a general covariance matrix, and let , Sn=X1+...+Xn. The asymptotics of as n--[infinity] are shown to be the same as for the independent case with the same lognormal marginals. In particular, for...

We show how, from a single simulation run, to estimate the ruin probabilities and their sensitivities (derivatives) in a classic insurance risk model under various distributions of the number of claims and the claim size. Similar analysis is given for the tail probabilities of the accumulated...

A risk process with constant premium rate $c$ and Poisson arrivals of claims is considered. A threshold $r$ is defined for claim interarrival times, such that if $k$ consecutive interarrival times are larger than $r$, then the next claim has distribution $G$. Otherwise, the claim size...