The ruin time under the Sparre-Andersen dual model

In this paper, we study the Sparre-Andersen dual risk model in which the times between positive gains are independently and identically distributed and have a generalized Erlang-n distribution. An important difference between this model and some other models such as the Erlang-n dual risk model is that the roots to the generalized Lundberg's equation are not necessarily distinct. Hence, we derive an explicit expression for the Laplace transform of the ruin time, which involves multiple roots. Also, we apply our approach for obtaining the expected discounted dividends when the threshold-dividend strategy discussed by Ng (2009) is implemented under the Sparre-Andersen model with Erlang-n distribution of the inter-event times. In particular, we derive an explicit form of the expected discounted dividends when jump sizes are exponential.