In this paper a one-dimensional surplus process is considered with
a certain Sparre Andersen type dependence structure under general interclaim
times distribution and correlated phase-type claim sizes. The
Laplace transform of the time to ruin under such a model is obtained as
the solution of a fixed-point problem, under both the zero-delayed and the
delayed cases. An efficient algorithm for solving the fixed-point problem
is derived together with bounds that illustrate the quality of the approximation.
A two-dimensional risk model is analyzed under a bailout type
strategy with both fixed and variable costs and a dependence structure of
the proposed type. Numerical examples and ideas for future research are
presented at the end of the paper.