Reserve-dependent surrender rates

We study the modelling and valuation of surrender and other behavioural options in life insurance and pension. We place ourselves in between the two extremes of optimal and arbitrary interventions by the policyholders. We present a model where one single parameter reflects the extent of rationality among policyholders. This presentation includes conditions which ensure that when the parameter goes to infinity contract values converge to the values corresponding to policyholders exhibiting optimal behaviour. When expenses are taken into account we lose the duality between the policyholder’s valuation of the contract and what we speak of as the market reserve. We include this in our model, and we give an upper bound for the difference between the value when the policyholder behaves optimally from her own point of view and the worst case market reserve from the pension fund point of view. In a series of numerical examples we illustrate the impact of the rationality parameter on the contract values.