This article provides a rigorous asymptotic analysis of long-term growth rates under both proportional and Morton-Pliska transaction costs. We consider a general incomplete financial market with an unspanned Markov factor process that includes the Heston stochastic volatility model and the...

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...

In a fully general semimartingale setting, this article establishes existence, uniqueness, monotonicity, concavity, and a utility gradient inequality for continuous-time recursive utility in the Epstein-Zin parametrization with relative risk aversion $\gamma$ and elasticity of intertemporal...

Motivated by the modeling of liquidity risk in fund management in a dynamic setting, we propose and investigate a class of time series models with generalized Pareto marginals: the autoregressive generalized Pareto process (ARGP), a modified ARGP (MARGP) and a thresholded ARGP (TARGP). These...

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...

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