Asymptotic Ruin Probabilities of the Renewal Model with Constant Interest Force and Regular Variation

Klüppelberg and Stadtmüller (1998, Scand. Actuar. J., no. 1, 49{58) obtained a simple asymptotic formula for the ruin probability of the classical model with constant interest force and regularly varying tailed claims. This short note extends their result to the renewal model. The proof is based on a result of Resnick and Willekens (1991, Comm. Statist. Stochastic Models 7, no. 4, 511{525)

The Finite Time Ruin Probability of the Compound Poisson Model with Constant Interest Force

In this paper we establish a simple asymptotic formula with respect to large initial surplus for thefinite time ruin probability of the compound Poisson model with constant interest force and subexponential claims. The formula is consistent with known results for the ultimate ruin probability and, in particular, it is uniform for all time horizons when the claim size distribution is regularly varying tailed

Finite and Infinite Time Ruin Probabilities in the Presence of Stochastic Returns on Investments

This paper investigates the finite and infinite time ruin probabilities in a discrete time stochastic economic environment. Under the assumption that the insurance risk - the total net loss within one time period - is extended-regularly-varying or rapidly varying tailed, various precise estimates for the ruin probabilities are derived. In particular, some estimates obtained are uniform with respect to the time horizon, hence apply for the case of infinite time ruin

Introducing a Dependence Structure to the Occurences in Studying Precise Large Deviations for the Total Claim Amount

In this paper we study precise large deviations for a compound sum of claims, in which the claims arrive in groups and the claim numbers in the groups may follow a certain negative dependence structure. We try to build a platform both for the classical large deviation theory and for the modern stochastic ordering theory

Asymptotics of Random Contractions

In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.Comment: 25 page