Practical Loss Reserving Method with Stochastic Development Factors

The paper presents a theoretical framework for measuring the inherent statistical variability of the loss development process. Chain ladder loss development factors are assumed to follow a LogNormal, Log Gamma or Log Inverse Gaussian distribution. From this, the conditional distribution of ultimate losses for each accident year is developed, and its parameters are estimated. By use of simulation, the distribution for the usual loss development triangle can also be calculated. Approximation formulae for the tail behavior of the distribution of ultimate losses of the trapezium are presented. In modelling the conditional distribution of ultimate losses, one can obtain an unbiased estimate of the mean of the total outstanding reserve, percentiles of the conditional distribution of reserves, which are required for solvency issues, and confidence intervals, which provide a measure of accuracy about the point estimate. The use of asymptotic formulae allows for statements about the probability of ruin without the need to simulate the distribution of losses. Other key words: reserving.