Solving Life Cycle Problems With Biometric Risk by Artificial Insurance Markets

We establish a powerful method to solve the life-cycle consumption choice problem of an individual facing biometric risks that are uninsurable. Problems of this type are notoriously hard to solve and closed-form solutions are unknown. The solution is obtained by optimizing over a parametrized family of consumption strategies. Each of these strategies is the optimal consumption strategy derived in closed form in an artificial market where the individual has access to fully flexible insurance contracts. In settings with mortality risk, critical illness risk and habit formation, our solution method outperforms the well-established finite difference approach both in running time and in precision. In contrast to the existing literature, our method also produces a closed-form consumption strategy, with some parameters determined in a numerical optimization