  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 company in terms of insurance parameters namely the premium,
total number of the insured, average loss claims etc. We restrict ourselves to
a single insurance class the so-called automobile insurance. We show the
existence a crossover premium p_c below which the company is loss-making. Above
p_c, we also give detailed statistical analysis of the company's financial
status and obtain the predicted profit along with the corresponding risk as
well as ruin probability in terms of premium. Furthermore we obtain the optimal
premium p_{opt} which maximizes the company's profit.
