The empirically observed hump-shaped pattern in individuals' consumption over their life cycle cannot be explained by the classical consumption-savings model. We explicitly solve an extended model with utility depending on both consumption and leisure and with endogenous educational decisions...

The observed hump-shaped life-cycle pattern in individuals' consumption cannot be explained by the classical consumption-savings model. The consensus explanation is that the hump is caused by constraints and unspanned risks. However, we explicitly show that the consumption hump naturally emerges...

In an incomplete market we study the optimal consumption-portfolio decision of an investor with recursive preferences of Epstein-Zin type. Applying a classical dynamic programming approach, we formulate the associated Hamilton-Jacobi-Bellman equation and provide a suitable verification theorem....

This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that...

This paper studies the life cycle consumption-investment-insurance problem of a family. The wage earner faces the risk of a health shock that significantly increases his probability of dying. The family can buy term life insurance with realistic features. In particular, the available contracts...

This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that...

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...