Optimal Dividends In The Perturbed Dual Model With Threshold Dividend Strategy

In the dual model, the surplus of a company is a levy process with sample paths that are skip-free downwards. In this paper, with a dividend threshold, the aggregate gains process is the sum of a shifted compound Poisson process and a in-dependent Winer process. We derive a set of integro-differential equations satisfied by the expected total discounted dividends until ruin and show how the equation can be solved by using only one of the two integro-differential equation. The cases where profits follow a mixture of exponential distributions are then solved and the discussion for the cases of a general profit distribution follows by the use of laplace transforms. We illustrate how the optimal threshold level that maximizes the ex-pected total discounted dividends until ruin can be obtained.