We formulate and analyze a mathematical framework for continuous-time mean field games with finitely many states and common noise. The key insight is that we can circumvent the master equation and reduce the mean field equilibrium to a system of forward-backward systems of (random) ordinary...

We extend the branching diffusion Monte Carlo method of Henry-Labordère e.a. [2019] to the case of parabolic PDEs with mixed local-nonlocal analytic nonlinearities. We investigate branching diffusion representations of classical solutions, and we provide sufficient conditions under which the...

This paper establishes existence of optimal controls for a general stochastic impulse control problem. For this, the value function is characterized as the pointwise minimum of a set of superharmonic functions, as the unique continuous viscosity solution of the quasi-variational inequalities,...

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...

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...

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...