A Note on the Risk Model with Dependence and Capital Injections

The note considers a risk model with dependence and capital injections, where the dependence structure is modeled by a Farlie-Gumbel-Morgenstern copula. In the risk model, the initial surplus starts from a level u \(\ge\) h, where h > 0 is a fix constant. The author derives an expression for the Laplace transform of the Gerber-Shiu function. In particular, an explicit formula for the Gerber-Shiu function is obtained when the initial surplus is h.