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 nth 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.
"Dividend Problems in the Diffusion Model with Interest and Exponentially Distributed Observation Time." J. Appl. Math. 2014 1 - 6, 2014. https://doi.org/10.1155/2014/814835