The growing relevance of risk-based valuations of insurance contracts has stimulated the extension of the traditional deterministic lapse rate models towards a dynamic modelling. A popular dynamic model uses deterministic lapse rates as base rates and dynamic adjustment factors, generally assuming a relationship between lapses and one or more economic factors to describe policyholder behaviour. This relationship is generally represented by an S-Shaped function. This implies a monotonic increase in lapse rate by increasing the economic variable, usually set equal to a “market spread” between a benchmark rate and the policy crediting rate. In this paper, we assume a different policyholder behaviour, based on the assumption that the policyholder does not modify his/her behaviour for small values of the market spread. Hence, for a better description of such behaviour, the double-sigmoid function appears to be more adequate. The double-sigmoid function is obtained as a combination of two logits in their sum or product. Theoretical features and practical applications of the model are discussed.

保险合同基于风险的估值日益增长的相关性刺激了传统的确定性失效率模型向动态建模的扩展。流行的动态模型使用确定性失效率作为基本比率和动态调整因素，通常假设失效与一个或多个经济因素之间的关系来描述保单持有人的行为。这种关系通常由 S 形函数表示。这意味着通过增加经济变量来单调增加失效率，经济变量通常设置为等于基准利率和政策贷记利率之间的“市场价差”。在本文中，我们假设不同的保单持有人行为，基于这样的假设，即保单持有人不会因市场价差的小值而改变他/她的行为。因此，为了更好地描述这种行为，双 sigmoid 函数似乎更合适。双 sigmoid 函数是作为两个 logits 的总和或乘积的组合获得的。讨论了该模型的理论特点和实际应用。