International Journal of Information Engineering and Electronic Business(IJIEEB)

ISSN: 2074-9023 (Print), ISSN: 2074-9031 (Online)

Published By: MECS Press

IJIEEB Vol.2, No.2, Dec. 2010

Some Results on Optimal Dividend Problem in Two Risk Models

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Shuaiqi Zhang

Index Terms

Optimal dividend,solvency constraints,compound Poisson risk model, compound Poisson risk model perturbed by diffusion


The compound Poisson risk model and the compound Poisson risk model perturbed by diffusion are considered in the presence of a dividend barrier with solvency constraints. Moreover, it extends the known result due to [1]. Ref. [1] finds the optimal dividend policy is of a barrier type for a jump-diffusion model with exponentially distributed jumps. In this paper, it turns out that there can be two different solutions depending on the model’s parameters. Furthermore, an interesting result is given: the proportional transaction cost has no effect on the dividend barrier. The objective of the corporation is to maximize the cumulative expected discounted dividends payout with solvency constraints before the time of ruin. It is well known that under some reasonable assumptions, optimal dividend strategy is a barrier strategy, i.e., there is a level b1(b2) so that whenever surplus goes above the level b1(b2), the excess is paid out as dividends. However, the optimal level b1(b2) may be unacceptably low from a solvency point of view. Therefore, some constraints should imposed on an insurance company such as to pay out dividends unless the surplus has reached a level 1505097046917402.png . We show that in this case a barrier strategy at 1505097102788651.png is optimal.

Cite This Paper

Shuaiqi Zhang,"Some Results on Optimal Dividend Problem in Two Risk Models", IJIEEB, vol.2, no.2, pp.24-30, 2010.


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