An Exact Solution for the Optimal Stop Loss Limit
针对团体寿险合同中的止损限额问题，在特定假设下推导出最优自留额的精确解析解，结果与实务观察吻合，对选择最优免赔额也有参考价值。
This paper examines a specialized situation where the insured can compute an exact analytical value for the optimim stop loss limit. The results may be of some interest in the case of a group life insurance contract with a stop loss limit. I lntro(ductionl The purpose of this note is to present an exact solution to the problem of determining the optimal retention level or stop-loss limit under a stop-loss insurance arrangement. The exact result conforms well to what is observed in practice under group life insured arrangements and is of some mathematical interest in its own right. The assumptions invoked to derive the results are somewhat specialized. Although this problem is couched in terms of group life insurance, certain aspects of our approach are of more general application and could be used, for example, in the selection of an optimal deductible. The motivation for this problem arises from the paper by Boyle and Mao (1982) which should be consulted for additional background. In the next Section we set up the general framework within which we are working, and in Section 3 the specialized assumptions with which we work are introduced. The optimal stop-loss limit under these assumptions can be obtained exactly even though it is the solution of a complicated non-linear equation. The detailed mathematical manipulations are left to the appendix. The final Section discusses the result. 2. General Framewvork The notation used follows that of Boyle and Mao (1982). Both the insurer and insured agree on the probability distribution of losses. Problems of moral hazard and adverse selections are ignored. The insured's problem is to select the optimal stop-loss limit' which will be a function of: Phelim P. Boyle is a Professor of Finance in the Accounting Group at the University of Waterloo. He is also a Professor of Statistics and Actuarial Science at the same University. He has published widely on topics in finance, insurance and actuarial science. Jennifer Mao is a Ph.D. student in Finance at the University of British Columbia. Her research interests include agency theory, insurance and alternative financial institutions. The authors appreciate the thoughtful comments of the referees on an earlier version of this paper. ' Note that the more general problem involves the selection of the optimal contract c . f. Raviv (1979). We tackle a much more restricted problem here.