A direct approach to the discounted penalty function

This paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closed-form expressions are obtained in the special case in which the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series of new results can be obtained with ease. Subsequently, certain results of Gerber and Shiu [H. U. Gerber and E. S. W. Shiu, North American Actuarial Journal 2(1): 48–78 (1998)] can be reproduced. The two-step approach is also applied when an independent Wiener process is added to the surplus process. Certain results are related to Zhang et al. [Z. Zhang, H. Yang, and S. Li, Journal of Computational and Applied Mathematics 233: 1773–1 784 (2010)], which uses different methods.

Optimal dividend strategies for a compound Poisson risk process under transaction costs and power utility

We characterize the value function of maximizing the total discounted utility of dividend payments for a compound Poisson insurance risk model when strictly positive transaction costs are included, leading to an impulse control problem. We illustrate that well known simple strategies can be optimal in the case of exponential claim amounts. Finally we develop a numerical procedure to deal with general claim amount distributions.

The joint influence of gender and amount of smoking on weight gain one year after smoking cessation.

Weight gain is often associated with smoking cessation and may discourage smokers from quitting. This study estimated the weight gained one year after smoking cessation and examined the risk factors associated with weight gain in order to identify socio-demographic groups at higher risk of increased weight after quitting. We analyzed data from 750 adults in two randomized controlled studies that included smokers motivated to quit and found a gradient in weight gain according to the actual duration of abstinence during follow-up. Subjects who were abstinent for at least 40 weeks gained 4.6 kg (SD = 3.8) on average, compared to 1.2 kg (SD = 2.6) for those who were abstinent less than 20 weeks during the 1-year follow-up. Considering the duration of abstinence as an exposure variable, we found an age effect and a significant interaction between sex and the amount of smoking before quitting: younger subjects gained more weight than older subjects; among light smokers, men gained more weight on average than women one year after quitting, while the opposite was observed among heavy smokers. Young women smoking heavily at baseline had the highest risk of weight gain after quitting.

On the efficient evaluation of ruin probabilities for completely monotone claim size distributions

In this paper we propose a highly accurate approximation procedure for ruin probabilities in the classical collective risk model, which is based on a quadrature/rational approximation procedure proposed in [2]. For a certain class of claim size distributions (which contains the completely monotone distributions) we give a theoretical justification for the method. We also show that under weaker assumptions on the claim size distribution, the method may still perform reasonably well in some cases. This in particular provides an efficient alternative to a related method proposed in [3]. A number of numerical illustrations for the performance of this procedure is provided for both completely monotone and other types of random variables.