Pure risk premiums under deductibles. A quantitative management in actuarial practice

It is common practice in most insurance lines for the coverage to be restricted by a deductible. In the paper we investigate the influence of deductibles on pure risk premiums. We derive simple but practical formulae for premiums under franchise, fix amount, proportional, limited proportional and disappearing deductibles in terms of the limited expected value function. Next, we apply the results to typical loss distributions, i.e. lognormal, Pareto, Burr, Weibull and gamma. Finally, we analyse a loss data of one of the power companies. We fit distributions to the data and show how the choice of the distribution and a deductible influences the premium.