A STOCHASTIC SIMULATION MODEL FOR REINSURANCE DECISION MAKING BY CEDING COMPANIES
It is known how the different forms of reinsurance must perform in theory but in practical use, because of the multitude of parameters involved, the complexity is such that it is impossible to identify whether a contract is or is not optimal. The interactions between an insurer's retention policy, the ceding and profitsharing commissions paid to this company, and its profitability, are very complex. The purpose of this study is to develop a model which will help management evaluate and choose among a variety of available sets of reinsurance arrangements. The model must, therefore, provide information on the impact of a particular set of reinsurance contracts and treaties on the company's operating results and net worth. More specifically, the information produced by the model refers to (1)the expected net cost and the standarddeviation of net cost of each arrangement within a given strategy, (2)the probability distribution of netunderwriting results in a given line of insurance, and (3)the probability distributions of the company's operating results and net worth. Because of the complexity involved in the design of a model which would analyze the reinsurance strategies simultaneously in all lines of business underwritten by a company, the study is limited to fire and earthquake risks insurance. The methodology adopted is to build a mathematical framework which is then used in a computer simulation model to give an estimate of the probability distribution of next period financial results of an insurer. In a first step, the simulation model generates, for a large number of repetitions of next year experience, the claims from each risk insured against fire and earthquake losses. This claim experience is then used repetitively to analyze the impact of various reinsurance strategies on reinsurance costs and on the financial results of a company. The MonteCarlo technique is used in the simulation portion of the model. The statistical analysis necessary to build the model is based on data that was provided by Seguros Caracas, the largest Venezuelan primary insurer and shareholder of the Reaseguradora Nacional de Venezuela, the financial sponsor of the study. Several decisionmaking criteria are presented: (1)dominance in a meanvariance sense, (2)ratios of risk reduction per unit of expected profit or net worth reduction, (3)ruin probabilities, and (4)utility theory. The ranking of the alternatives can vary from one criteria to another. For example, the ranking according to the "ratio method" of comparison depends on which variable is used to compute the ratios. The fire and earthquake underwriting results, the overall operating results, and the net worth value were the choices suggested. With respect to utility theory, the illustrations were made using an exponential utility function. The results suggest that much care should be used when selecting a risk aversion parameter. The ruin probabilities were estimated based on the normal approximation method and the normal power method. Although the model was designed with emphasis on its use by a ceding company, it can also be helpful to the reinsurer in its determination of the costing, ceding commission, and profitsharing commission parameters that should be required for a given arrangement. The use of the model by both parties would not necessarily produce an immediate agreement on those parameters, since each of them can use their own estimates of the frequency and severity distributions' shapes and parameters and because each of them are very likely to have different utility preferences.
Year of publication: 
19810101


Authors:  ROY, YVES 
Publisher: 
ScholarlyCommons 
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