In the compound Poisson insurance risk model under a dividend barrier strategy, this paper aims to analyze jointly the aggregate discounted claim amounts until ruin and the total discounted dividends until ruin, which represent the insurer’s payments to its policyholders and shareholders, respectively. To this end, we introduce a Gerber–Shiu-type function, which further incorporates the higher ...

In this paper, we study ruin in a perturbed compound Poisson risk process under stochastic interest force and constant interest force. By using the technique of stochastic control, we show that the ruin probability in the perturbed risk model is always twice continuously differentiable provided that claim sizes have continuous density functions. In the perturbed risk model, ruin may be caused b...

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...

Assume that the surplus of an insurer follows a jump­diffusion process and the insurer would invest its surplus in a risky asset, whose prices are modelled by a geometric Brow­ nian motion. The resulting surplus for the insurer is called as a jump­diffusion surplus process compounded by the geometric Brownian motion. In this resulting surplus process, ruin may be caused by a claim or by oscilla...

We consider several one-period reinsurance models and derive a rule which minimizes the ruin probability of the cedent for a fixed reinsurance risk premium. The premium is calculated according to the economic principle, generalized zero-utility principle, Esscher principle or mean-variance principles. It turns out that a truncated stop loss is an optimal treaty in the class of all reinsurance c...

This paper investigates the optimal sampling and the speed-up obtained through sampling for the sampled OneMax problem. Theoretical and experimental analyses are given for three different population-sizing models: the decision-making model, the gambler’s ruin model, and the fixed population-sizing model. The results suggest that, when the desired solution quality is fixed to a high value, the d...