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

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.