Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest

Jun Cai, Hans Gerber and Hailiang Yang

North American Actuarial Journal, 2006, vol. 10, issue 2, 94-108

Abstract: In the absence of investment and dividend payments, the surplus is modeled by a Brownian motion. But now assume that the surplus earns investment income at a constant rate of credit interest. Dividends are paid to the shareholders according to a barrier strategy. It is shown how the expected discounted value of the dividends and the optimal dividend barrier can be calculated; Kummer’s confluent hypergeometric differential equation plays a key role in this context. An alternative assumption is that business can go on after ruin, as long as it is profitable. When the surplus is negative, a higher rate of debit interest is applied. Several numerical examples document the influence of the parameters on the optimal dividend strategy.

Date: 2006
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DOI: 10.1080/10920277.2006.10596250

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