This thesis deals with 3 important aspects of optimal investment in real-world financial markets: taxes, crashes, and illiquidity. An introductory chapter reviews the portfolio problem in its historical context and motivates the theme of this work: We extend the standard modelling framework to...

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

We show that the optimal consumption of an individual over the life cycle can have the hump shape (inverted U-shape) observed empirically if the preferences of the individual exhibit internal habit formation. In the absence of habit formation, an impatient individual would prefer a decreasing...

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 continuous-time optimal consumption and investment with Epstein-Zin recursive preferences in incomplete markets. We develop a novel approach that rigorously constructs the solution of the associated Hamilton-Jacobi-Bellman equation by a fixed point argument and makes it possible to...