The Gerber-Shiu discounted penalty function is considered for a class of delayed renewal risk processes. Special cases of the model include the stationary renewal risk model and the situation where the time until the first claim is exponentially distributed. A mathematically tractable formula is derived for the Gerber-Shiu function, and consequently for quantities associated with the deficit at...

In this paper we extend the results in Lin and Willmot (1999 Insurance: Mathematics and Economics 25, 63–84) to properties related to the joint and marginal moments of the time of ruin, the surplus before the time of ruin, and the deficit at the time of ruin. We use an approach developed in Lin and Willmot (1999), under which the solution to a defective renewal equation is expressed in terms of...

this paper mainly considers a nonstandard risk model with a constant interest rate‎, ‎where both the claim sizes and the inter-arrival times follow some certain dependence structures‎. ‎when the claim sizes are dominatedly varying-tailed‎, ‎asymptotics for the infinite time ruin probability of the above dependent risk model have been given‎.

This paper studies ruin probabilities in two discrete-time risk models with premiums, claims and rates of interest modelled by three autoregressive moving average processes. Generalized Lundberg inequalities for ruin probabilities are derived by using recursive technique. A numerical example is given to illustrate the applications of these probability inequalities. Keywords—Lundberg inequality,...

In this paper, we consider a dual risk process which can be used to model the surplus of a business that invests money constantly and earns gains randomly in both time and amount. The occurrences of the gains and their amounts are assumed follow a semi-Markovian structure (e.g. Reinhard (1984)). We analyze a quantity resembling the Gerber-Shiu expected discounted penalty function (Gerber and Sh...

We focus on numerical evaluation of some quantities of interest in ruin theory, and on the practical use of the fast Fourier transform algorithm (FFT) in this context. We discuss the general application of the FFT for stochastic models, and we illustrate this by looking again at the probability of ruin in the classical risk model and by extending this approach to evaluation of the first moment ...

In this paper we consider a compound Poisson risk model where the insurer earns credit interest at a constant rate if the surplus is positive and pays out debit interest at another constant rate if the surplus is negative. Absolute ruin occurs at the moment when the surplus first drops below a critical value (a negative constant). We study the asymptotic properties of the absolute ruin probabil...