关于健康保险负债的市场一致估值

On the market-consistent valuation of health insurance liabilities

Up to inflation, the basic cash flow associated to health insurance policies is independent from capital markets. It has therefore been common to calculate the Best Estimate based on a deterministic approach. However, in the light of volatile inflation dynamics in recent years, it has become more popular to use stochastic models for the Best Estimate of health insurance policies. In this article, we show that this stochastic approach is preferable and provide a framework to efficiently evaluate a large stock of health insurance policies. More precisely, we first prove that the Best Estimate of a life-long health insurance policy depends on the choice of model for the interest and inflation rates. That is, the Best Estimate is not uniquely determined by the current nominal and real spot rates used to calibrate these type of models -- even without profit participation or the common practice of limiting premium adjustments. Second, we construct a valuation portfolio for life-long health insurance policies without the common industry practice of limiting the premium adjustments, decomposing the Best Estimate into 1.) deterministic coefficients derived from policy data and 2.) the prices of basis financial instruments that are independent of the individual policy data. Using this decomposition, the policies do not have to be tracked individually along each generated inflation path. This allows a very efficient evaluation of the Best Estimate for a large stock of policies with a stochastic model.