Use of chance-constrained programming techniques to determine optimal insurance deductible levels

With the increasing rate of product liability claims and dramatically escalating product liability insurance costs, many manufacturers are looking for alternative methods of dealing with these financial uncertainties. Manufacturers are turning to various forms of risk retention, such as complete self-insurance or partial self-insurance in the form of increased deductible levels. A chance-constrained linear programming model is formulated based on the assumed loss distributions parameters to optimize the deductible levels to minimize total costs. The model considers factors such as insurance premium costs under various pricing methods, varying number of losses, varying sizes of losses, and the degree of risk the manufacturer is willing to accept.;Using a collective risk model, the aggregate (per product line) loss distributions that are faced by the manufacturers are modeled as compound distributions. The number of losses can be characterized as either a Poisson or a negative binomial distribution, and the loss amounts can be modeled with a variety of continuous distributions. Depending on the value of the deductible level (the model's decision variable), the distribution of losses will be truncated. This truncation affects the manufacturer's loss distribution, as well as the insurance company's loss distribution which is used to determine premium costs. The model uses the first and second moments of both of these truncated distributions to create a nonlinear objective function and nonlinear constraints. The model is then solved using a standard nonlinear programming computer package. The effectiveness of the deductible in meeting the manufacturer's risk preferences is verified using Monte Carlo simulation techniques.;The applicability of the model to actual insurance situations was verified by presenting the model to a number of manufacturers and surveying their opinions as to the reasonableness and usefulness of the model.