We consider an optimal investment problem for an investor facing both constant and proportional transaction costs and study the limit as the constant cost tends to zero. Combining the stochastic Perron's method with stability arguments for viscosity solutions, we show that the value function...

We study the problem of maximizing expected utility of terminal wealth under constant and proportional transactions costs in a multidimensional market with prices driven by a factor process. We show that the value function is the unique viscosity solution of the associated quasi-variational...

We study a portfolio optimization problem in a market which is under the threat of crashes. At random times, the investor receives a warning that a crash in the risky asset might occur. We construct a strategy which renders the investor indifferent about an immediate crash of maximum size and no...

We study a portfolio optimization problem in a financial market which is under the threat of crashes. At random times, the investor receives warnings that a bubble has formed in the market which may lead to a crash in the risky asset. We propose a regime switching model for the warnings and we...

Building on an abstract framework for dynamic nonlinear expectations that comprises g-, G- and random G-expectations, we develop a theory of backward nonlinear expectation equations. We provide existence, uniqueness, and stability results and establish convergence of the associated discrete-time...

We study optimal portfolio decisions for a retail investor that faces proportional costs which are floored and capped at some minimal and maximal cost levels, respectively, in a classical Black-Scholes market. We provide a construction of optimal trading strategies and characterize the value...

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...