The observed hump-shaped life-cycle pattern in individuals' consumption cannot be explained by the classical consumption-savings model. We explicitly solve a model with utility of both consumption and leisure and with educational decisions affecting future wages. We show optimal consumption is...

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their "distance" to a reference local volatility model. In...

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....

We investigate worst-case optimal consumption and portfolio decisions under the threat of a market crash. In an infinite-horizon setting, we provide an explicit solution for constant relative risk aversion and establish a rigorous verification result. Moreover, we find a dual characterization of...

We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic di erential utility, as introduced by Du e and Epstein (1992), in the continuous-time limit of vanishing grid size