Simulation methods in ruin models with non-linear dividend barriers

Hansjörg Albrecher, Reinhold Kainhofer, Robert F. Tichy In the framework of classical risk theory we consider the process Rt = u+ c t− ∑N(t) i=1 Xi, where c is a constant premium density, N(t) denotes a homogeneous Poisson process with intensity λ which counts the claims up to time t, and the claim amounts Xi are iid random variables with distribution function F (y). In this context Rt represents the surplus of an insurance portfolio at time t and u = R0 denotes the initial capital (see e.g. Asmussen [3]). Furthermore we assume μ = E(Xi) < ∞ and c > λ ∫∞ 0 y dF (y). A reasonable modification of this model is the introduction of a (time-dependent) dividend barrier bt, i.e. whenever the surplus Rt reaches bt, dividends are paid out to the shareholders with intensity c−dbt and the surplus remains on the barrier, until the next claim occurs. Thus the risk process develops according to