Paper: arXiv 2410.07749

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced continuous-time stochastic optimal control, HJB PDEs, and Epstein–Zin preferences, representing dense mathematics. However, it focuses on theoretical derivations with limited numerical implementation and no backtesting or real-world data, placing it low on empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Determine optimal mutual insurance<br>against systematic longevity risk"] --> B["Methodology<br>Mathematical modeling of two collective<br>pension funds with differing risk preferences"]
  B --> C["Key Inputs<br>Systematic longevity risk assumption<br>Disparate risk preferences"]
  C --> D["Computational Process<br>Establish a market clearing condition<br>to facilitate the insurance exchange"]
  D --> E{"Comparison"}
  E -- "Preferences are<br>similar" --> F["Outcome<br>Little benefit from insurance<br>Base scheme is effectively optimal"]
  E -- "Preferences are<br>dissimilar" --> G["Outcome<br>Mutual insurance is beneficial"]
  F --> H["Final Finding<br>Insurance market exists even with<br>identical risks if preferences differ"]
  G --> H

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1 of 89 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.