Optimal mutual insurance against systematic longevity risk

TL;DR

This paper mathematically analyzes how two pension funds can mutually insure against systematic longevity risk through a market clearing condition, highlighting the impact of their risk preferences on insurance benefits.

Contribution

It introduces a formal framework for mutual insurance between pension funds against longevity risk, emphasizing the role of risk preferences and market conditions.

Findings

Mutual insurance is beneficial when funds have significantly different risk preferences.

The market clearing condition enables insurance exchange even with identical mortality risks.

Base schemes are nearly optimal if funds' preferences are similar.

Abstract

We mathematically demonstrate how and what it means for two collective pension funds to mutually insure one another against systematic longevity risk. The key equation that facilitates the exchange of insurance is a market clearing condition. This enables an insurance market to be established even if the two funds face the same mortality risk, so long as they have different risk preferences. Provided the preferences of the two funds are not too dissimilar, insurance provides little benefit, implying the base scheme is effectively optimal. When preferences vary significantly, insurance can be beneficial.