A stochastic model of mutual insurance under heterogeneous time preferences

Abstract

This research examines the premium control problem of a mutual insurance company when its policyholders have heterogeneous (or present-biased) time preferences. When decisions are made collectively by policyholders with diverse time preferences, utilitarian aggregation results in time-inconsistent time preferences. To address time inconsistency, we employ an intra-personal game theoretic framework and seek a time-consistent equilibrium strategy. The equilibrium strategy recommends collecting premiums at the minimal rate when the mutual insurer's reserve surpasses a specified threshold and at the maximal rate when it falls below this threshold. We find that higher heterogeneity (or equivalently, the decreasing impatience) of policyholders' time preferences will lead to lower reserve thresholds. Our model offers insights for mutual insurers to design premium policies when their policyholders have diverse time preferences.

Keywords: time-inconsistency, mutual insurance, heterogeneous time preference, present bias