The paper deals with the renewal equation governing the infinite-time ruin probability. It is emphasized as intended to be no more than a pleasant ramble through a few scattered results. An interesting connection between ruin probability and a recurslon formula for computation of the aggregate claims distribution is noted and discussed. The relation between danger of the claim size distribution...

In this paper, we show that the delayed Sparre Andersen insurance risk model in discrete time can be analyzed as a doubly infinite, right skip-free Markov chain. We then describe how matrix analytic methods can be used to establish a computational procedure for calculating the probability distributions associated with fundamental ruin-related quantities of interest, such as the time of ruin, th...

We start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X̂. Our methodology applies to the case when the dynamics of the aggregate claims process is a subordinator. From this expression, we easily deduce necessary and suffi...

In this paper we evaluate the probability of the discrete time Parisian ruin that occurs when surplus process stays below or at zero at least for some fixed duration of time d > 0. We identify expressions for the ruin probabilities within finite and infinite-time horizon. We also find their light and heavy-tailed asymptotics when initial reserves approach infinity. Finally, we calculate these p...

This paper investigates the finiteand 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 tailed or rapidly-varying tailed, various precise estimates for the ruin probabilities are derived. In particular, some estimates obtained are uniform wi...

Stop-loss reinsurance is a risk management tool that allows an insurance company to transfer part of their company. Ruin probabilities allow us measure the effect stop-loss on solvency primary insurer. They further permit calculation economic capital, or required initial capital hold, corresponding 99.5% value-at-risk its surplus. Specifically, we show under contract, ruin probability for insur...

We consider a risk process modelled as a compound Poisson process. We find the optimal dynamic unlimited excess of loss reinsurance strategy to minimize infinite time ruin probability, and prove the existence of a smooth solution of the corresponding HamiltonJacobi-Bellman equation as well as a verification theorem. Numerical examples with exponential, shifted exponential, and Pareto claims are...

This paper is concerned with several types of ruin probabilities for a multivariate compound Poisson risk model, where the claim size vector follows a multivariate phase type distribution. First, an explicit representation for the convolution of a multivariate phase type distribution is derived, and then an explicit formula for the ruin probability that the total claim surplus exceeds the total...