Determination of minimum initial capital using the Cramer-L undberg model and discrete time Bisection Ruin model

Abstract

The dissertation uses the classical Cramer-Lundberg model to find the minimum initial capital (MIC) required by a hypothetical insurance company in launching a new product line, or, for investors wishing to open a new insurance company with their expectations likely to follow those of the classical ruin model. The Poisson and exponential rate were taken as one and the probability of ruin taken as fixed (0.1, 0.2 or 0.3). The safety coefficient for each of the probabilities of ruin was taken as either 0.1 or 0.25 of the premium. A Brownian motion approximation to the compound Poisson aggregate claims model was also used. It was observed that there was a linear relationship between the the minimum initial surplus and the number of claims for the continuous time ultimate ruin model.Cramer’s approximation was considered as providing the most correct MIC whereas the Lundberg model provided a ceiling. The Brownian motion approximation was slightly higher than the values provided by the Lundberg model and this can be explained by the variance (higher moments) effect taken into account by the Brownian motion approximation. A discrete time model was also considered as that provided by Sattayatham et al (2013) where the bisection method was used to find the MIC. It was noticed that the MIC in this case was considerably smaller than those provided by the continuous case and this can be explained by the fact that the discrete case only requires non-ruin at integer durations. Therefore ruin can occur in between the intervals as long as there is no ruin at the integer duration. The curve of the discrete MIC against number of claims was curvilinear. There was no intersection of the curves for any of the methods.