Solving life-cycle problems with biometric risk by artificial insurance markets

Christoph Hambel, Holger Kraft and Claus Munk

Scandinavian Actuarial Journal, 2022, vol. 2022, issue 4, 307-327

Abstract: 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.

Date: 2022
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DOI: 10.1080/03461238.2021.1966831

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