In this paper we consider a risk process in which claim inter-arrival times have an Erlang(2) distribution. We consider the inÂ…nite time survival probability as a compound geometric random variableâ€¦ (More)

We consider a classical surplus process where the insurer can choose a different level of reinsurance at the start of each year. We assume the insurerâ€™s objective is to minimise the probability ofâ€¦ (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)

We derive a closed-form (infinite series) representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. This extends a recent result ofâ€¦ (More)

In the collective risk model we use the objective Bayesian approach to calculate predictive aggregate claims distributions. Very often this is equivalent to the profile predictive likelihoodâ€¦ (More)

In the Sparre Andersen risk model, we derive a general expression for h(u, x, y), the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is u. Thisâ€¦ (More)

We consider a classical surplus process modified by the payment of dividends when the insurerâ€™s surplus exceeds a threshold. We use a probabilistic argument to obtain general expressions for theâ€¦ (More)

We consider a compound Poisson risk model where part of the premium is paid to the shareholders as dividends when the surplus exceeds a specified threshold level. In this model, we are interested inâ€¦ (More)

We consider an insurer who has a fixed amount of funds allocated as the initial surplus for a risk portfolio, so that the probability of ultimate ruin for this portfolio is at a known level. Weâ€¦ (More)

Properties of the distribution of the deficit at ruin in the stationary renewal risk model are studied. A mixture representation for the conditional distribution of the deficit at ruin (given thatâ€¦ (More)