For a general class of risk models, the dividends-penalty identity is derived by probabilistic reasoning. This identity is the key for understanding and determining the optimal dividend barrier, which maximizes the difference between the expected present value of all dividends until ruin and the expected discounted value of a penalty at ruin (which is typically a function of the deficit at ruin...

We revisit the dividend payment problem in the dual model of Avanzi et al. ([2–4]). Using the !uctuation theory of spectrally positive Lévy processes, we give a short exposition in which we show the optimality of barrier strategies for all such Lévy processes. Moreover, we characterize the optimal barrier using the functional inverse of a scale function. We also consider the capital injection p...

In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and byclaims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer’s...

Yuzhen Wen and Chuancun Yin School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China Correspondence should be addressed to Yuzhen Wen, [email protected] Received 5 February 2012; Revised 16 April 2012; Accepted 20 April 2012 Academic Editor: Laurent Gosse Copyright q 2012 Y. Wen and C. Yin. This is an open access article distributed under the Creative Commons Attribu...

Assume that the surplus process of an insurance company is described by a general Lévy process and that possible dividend pay-outs to shareholders are restricted to random discrete times which are determined by an independent renewal process. Under this setting we show that the optimal dividend pay-out policy is a band-policy. If the renewal process is a Poisson process, it is further shown tha...

In a Lévy insurance risk model, under the assumption that the tail of the Lévy measure is log-convex, we show that either a horizontal barrier strategy or the take-the-money-and-run strategy maximizes, among all admissible strategies, the dividend payments subject to an affine penalty function at ruin. As a key step for the proof, we prove that, under the aforementioned condition on the jump me...

Effects of dividend policy on corporate financial growth, is a major concern of most entities. Whether dividends have an influence on the value of the firm, is an important question in dividend policy. This study aimed at investigating the effects of dividend policy on financial growth of media firms. The study was conducted in Nairobi at The Nation media Group Headquarters. Respondents were se...

The expected present value of dividends is one the classical stability criteria in actuarial risk theory. In this paper, we consider two-layer $ (a, b) dividend strategy when process modeled by a spectrally negative Lévy process, such has an increasing rate surplus exceeds level a>0 $, and all excess over b>a as lump sum payments. Using fluctuation identities scale functions, obtain expli...