Solving Life-cycle Problems with Biometric Risk by Artificial Insurance Markets

Christoph Hambel*, Holger Kraft, Claus Munk

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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We study canonical consumption-savings problems of an individual involving uninsurable biometric risk. These problems are important in many applications from insurance economics and actuarial science. Since biometric risk is uninsurable, closed-form solutions do not exist and thus the problems must be approached by numerical methods. We propose a powerful approach where the solution is obtained by optimizing over a parametrized family of consumption strategies. In settings with mortality risk, critical illness risk, and habit formation, our solution method outperforms the well-established finite-difference approach both in run time and in precision. Our method also delivers a precision measure and closed-form representations of the optimal controls.
Original languageEnglish
JournalScandinavian Actuarial Journal
Issue number4
Pages (from-to)307-327
Number of pages21
Publication statusPublished - May 2022

Bibliographical note

Published online: 19 Aug 2021.


  • Dynamic programming
  • Life-cycle models
  • Biometric risk
  • Insurance
  • Habit formation

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