We study optimal portfolio decisions for a retail investor that faces a strictly positive transaction cost in a classical Black‐Scholes market. We provide a construction of optimal trading strategies and characterize the value function as the unique viscosity solution of the associated...

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...

We revisit the problem of maximizing expected utility of terminal wealth in a Black-Scholes market with proportional transaction costs. While it is known that the value function of this problem is the unique viscosity solution of the HJB equation and that the HJB equation admits a classical...

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 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...