Abstract

  We present an analytical study of an insurance company. We model the company’s performance on a statistical basis and evaluate the predicted annual income of the com- pany in terms of insurance parameters namely the premium, the total number of insured, average loss claims etc. We restrict ourselves to a single insurance class the so-called au- tomobile insurance. We show the existence of a crossover premium pc below which the company is operating at a loss. Above pc , we also give a detailed statistical analysis of the company’s financial status and obtain the predicted profit along with the corre- sponding risk as well as ruin probability in terms of premium. Furthermore we obtain the optimal premium popt which maximizes the company’s profit.