The dilemma between dividends and safety and a generalization of the Lundberg-Cramér formulas

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Abstract
The question how a company should payout dividends has led to some controversy (see [2], p. 164). At first sight it seems that the payment of dividends could be reconciled with the safety of a company by the following rule: “At any payment date, determine the dividend such that the resulting probability of ruin is equal to some given level e.” But, as De Finetti points out (see [5]), repeated application of this rule leads to eventual ruin of the company (with probability one). Alternatively, he suggested that dividends could be determined in order to maximize the expected sum of the discounted dividends. This idea has inspired a series of writers, among others Borch, Morrill, Miyasawa (the reader will find references in [2], pp. 164–178, and [9], pp. 163–166).

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