Dividend problems in the diffusion model with interest and exponentially distributed observation time (Q1714774)

Summary: Consider dividend problems in the diffusion model with interest and exponentially distributed observation time where dividends are paid according to a barrier strategy. Assume that dividends can only be paid with a certain probability at each point of time; that is, on each observation, if the surplus exceeds the barrier level, the excess is paid as dividend. In this paper, integrodifferential equations for the moment-generating function, the \(n\)th moment function, and the Laplace transform of ruin time are derived; explicit expressions for the expected discounted dividends paid until ruin and the Laplace transform of ruin time are also obtained.