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The Scientific World Journal
Volume 2015 (2015), Article ID 354129, 9 pages
Research Article

Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process

1School of Mathematical Sciences, Qufu Normal University, Shandong 273165, China
2Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong

Received 28 May 2014; Accepted 9 November 2014

Academic Editor: Taizhong Hu

Copyright © 2015 Chuancun Yin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy.