Reserve-Dependent Surrender

TL;DR

This paper introduces a differential equation-based method to model and value life insurance contracts with policyholder surrender behavior, balancing between arbitrary and optimal actions through a rationality parameter.

Contribution

It presents a novel approximation technique for contract valuation considering varying policyholder rationality, with conditions ensuring model consistency and convergence.

Findings

The rationality parameter significantly affects contract values.

The method provides a simple way to interpolate between arbitrary and optimal behavior.

Numerical examples demonstrate the impact of policyholder rationality on valuation.

Abstract

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 completely arbitrary intervention and optimal intervention by the policyholder. We present a method that is based on differential equations and that can be used to approximate contract values when policyholders exhibit optimal behaviour. This presentation includes a specification of sufficient conditions for both consistency of the model and convergence of the contract values. When not going to the limit in the approximation we obtain a technique for balancing off arbitrary and optimal behaviour in a simple, intuitive way. This leads to our suggestions for intervention models where one single parameter reflects the extent of rationality among policyholders. In a series of numerical examples we illustrate the impact of the rationality parameter on the contract values.