Convexity of ruin probability and optimal dividend strategies for a general Levy process

Mathematics – Probability

Scientific paper

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24 pages, corrected some typos

Scientific paper

We continue the recent work of Yuen and Yin (Mathematical and Computer Modelling 53 (2011): 1700-1707) to study the optimal dividends problem for a company whose cash reserves follow a general Levy process with two-sided jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of bankruptcy. Under appropriate conditions, we obtain the convexity properties of probability of ruin and the generalized scale function. Subsequently we investigate when the dividend policy that is optimal among all admissible ones takes the form of a barrier strategy.

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