Statistical Modeling Techniques for Reserve Ranges: A Simulation Approach

The goal of this paper is to develop simple, quantitative methods to generate a range of reserves for an aggregate insurance portfolio, and provide a basis for selecting the best estimate of the aggregate reserves, given assumptions by accident period or by line of business. The basic assumption of the paper is that the range of reserves generated by the application of various actuarial techniques (for example projection of paid losses, projection of incurred losses, Bornhuetter-Ferguson techniques) can be used to generate parameters for loss distributions by accident year or by line of business. Accident year or line of business parameters generated based on the reserve projections are then used, along with simulation techniques, to generate a range for the aggregate reserves. The first section of the paper describes some of the current statistical, and ad-hoc methodologies used by actuaries to generate reserve ranges. The second section describes some distribution functions that could be used in the simulation process. It focuses on four relatively simple and common distribution functions (uniform, triangle, normal, and lognormal) and describes situations where they would be most suitable. The third section describes the simulation methodology and explores techniques for generating the parameters to be used in the actual simulations. In addition, it explores the issue of what would be an appropriate number of simulations. The final section presents results from simulations for three different types of insurance portfolios. Results are plotted graphically, and comparisons are made of the simulated and unsimulated ranges. Keywords: Simulation, Reserve Ranges, Aggregate Insurance Portfolios