Is sociality driven by the costs of dispersal or the benefits of philopatry? A role for kin-discrimination mechanisms.

The role of ecological constraints in promoting sociality is currently much debated. Using a direct-fitness approach, we show this role to depend on the kin-discrimination mechanisms underlying social interactions. Altruism cannot evolve under spatially based discrimination, unless ecological constraints prevent complete dispersal. Increasing constraints enhances both the proportion of philopatric (and thereby altruistic) individuals and the level of altruistic investments conceded in pairwise interactions. Familiarity-based discrimination, by contrast, allows philopatry and altruism to evolve at significant levels even in the absence of ecological constraints. Increasing constraints further enhances the proportion of philopatric (and thereby altruistic) individuals but not the level of altruism conceded. Ecological constraints are thus more likely to affect social evolution in species in which restricted cognitive abilities, large group size, and/or limited period of associative learning force investments to be made on the basis of spatial cues.

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.