A sharing mechanism of investment outcome for interest-sensitive life insurance products

Abstract

As growing sales of insurance contracts with a saving feature, an issue of sharing investment outcome gets the attention of insurers and policyholders. This paper focuses on a systematic way of finding the sharing mechanism for an optimal contract design in such a way that a policyholder and an insurer maximize their expected utilities. We adopt the policyholder and the insurer as a principal and an agent, respectively, and regard a share of the investment performance as an incentive for the insurer to elicit efforts. As a result of this setting, the moral hazard issue generated from the insurer is unavoidable. For the purpose, the Holmstrom (1979)'s principal-agent model with limited observability of the insurer's action plays a leading role in resolving a pie-cutting problem. Under our model assumption, the sharing mechanism states that a portion of the outcome belonging to the insurer is a nondecreasing function of the excess of the portfolio return over a benchmark return when the two parties are risk-averse. In particular, the sensitivity of the sharing portion has an S-shape curve which is consistent with the insurer's risk propensity. An empirical study based on companies' portfolio attributes and crediting rates verifies that our theoretical findings are consistent with statistically significant results. In particular, we confirm that the bargaining power of the insurer has a considerable impact on the sharing mechanism as it is theoretically important.