This paper considers the stationary and the ordinary discrete renewal risk models. The main result is an expression of the Gerberâ€“Shiu discounted penalty function in the stationary model in terms ofâ€¦ (More)

The defective renewal equation satisfied by the Gerber-Shiu discounted penalty function in the renewal risk model with arbitrary interclaim times is analyzed. The ladder height distribution is shownâ€¦ (More)

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 whereâ€¦ (More)

For any function f on the non-negative integers, we can evaluate the cumulative function Î“f given by Î“f(s) = âˆ‘s x=0 f(x) from the values of f by the recursion Î“f(s) = Î“f(sâˆ’1)+f(s). Analogously we canâ€¦ (More)

A generalized class of Tijms-type approximations for ruin and waiting time probabilities is discussed. Conditions are obtained under which the correct asymptotic right tail behavior is exhibited,â€¦ (More)

We describe an approach to the evaluation of the moments of the time of ruin in the classical Poisson risk model. The methodology employed involves the expression of these moments in terms of linearâ€¦ (More)

In this paper we extend the results in Lin and Willmot (2000 Insurance: Mathematics and Economics 27, 19-44) to these based on the surplus process perturbed by diffusion. We first derive theâ€¦ (More)

In this paper, we discuss the distributional properties of random sums. We first derive conditions under which the distribution of a binomial sum is PF2 and then show under the same conditions theâ€¦ (More)

We derive an expression for the density of the time to ruin in the classical risk model by inverting its Laplace transform. We then apply the result when the individual claim amount distribution is aâ€¦ (More)