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ScientificWorldJournal. 2015;2015:354129. doi: 10.1155/2015/354129. Epub 2015 Aug 13.

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

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


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.

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