Modeling of the Negative Surplus in Insurance

Abstract. An insurance activity model that allows to evaluate the duration of the negative surplus is presented in this paper. Assuming the surplus process as continuing if ruin occurs, we consider how long this process will stay below zero. The compound Poisson continuous time surplus process is used for the model development. Analytical formulas are obtained for estimating the expected value and the dispersion of both the number and the duration times of negative surpluses when individual claims amount is distributed according to the Gamma (α, β) distribution, with free choice of the parameters α ∈N and β > 0. We use simulation to verify the soundness of the analytical results, evaluating the performance of surplus process under various factors. An aggregate approach has been used for creation of formal description of insurer’s business process. The characteristics of the duration of the negative surplus are computed and compared with the theoretical approximate values obtained from the analytical expressions.