Das Institut für Mathematische Wirtschaftsforschung veranstaltet im Rahmen des Bielefeld Stochastic Afternoon regelmäßig Seminare zum Thema Finanzmathematik. Das Programm des aktuellen Semesters finden Sie hier.
Michael Barnett (Arizona State)
Titel: A Deep Learning Analysis of Climate Change, Innovation, and Uncertainty
Abstract: We study the implications of model uncertainty in a climate-economics framework with three types of capital: “dirty” capital that produces carbon emissions when used for production, “clean” capital that generates no emissions but is initially less productive than dirty capital, and knowledge capital that increases with R&D investment and leads to technological innovation in green sector productivity. To solve our high-dimensional, non-linear model framework we implement a neural-network-based global solution method. We show there are first-order impacts of model uncertainty on optimal decisions and social valuations in our integrated climate-economic-innovation framework. Accounting for interconnected uncertainty over climate dynamics, economic damages from climate change, and the arrival of a green technological change leads to substantial adjustments to investment in the different capital types in anticipation of technological change and the revelation of climate damage severity. This is joint work with William Brock, Lars Peter Hansen, Ruimeng Hu and Joseph Huang.
Antonis Papapantoleon (TU Delft)
Titel: Model-free and data driven methods in mathematical finance
Abstract: Academics, practitioners and regulators have understood that the classical paradigm in mathematical finance, where all computations are based on a single "correct" model, is flawed. Model-free methods, were computations are based on a variety of models, offer an alternative. More recently, these methods are driven by information available in financial markets. In this talk, we will discuss model-free and data driven methods and bounds and present how ideas from probability, statistics, optimal transport and optimization can be applied in this field.
Mitja Stadje (Ulm University)
Titel: Utility maximization under endogenous pricing
Abstract: We study the expected utility maximization problem of a large investor who is allowed to make transactions on tradable assets in an incomplete financial market with endogenous permanent market impacts. The asset prices are assumed to follow a nonlinear price curve quoted in the market as the utility indifference curve of a representative liquidity supplier. We show that optimality can be fully characterized via a system of coupled forward-backward stochastic differential equations (FBSDEs) which corresponds to a non-linear backward stochastic partial differential equation (BSPDE). We show existence of solutions to the optimal investment problem and the FBSDEs in the case where the driver function of the representative market maker grows at least quadratically or the utility function of the large investor falls faster than quadratically or is exponential. Furthermore, we derive smoothness results for the existence of solutions of BSPDEs. Examples are provided when the market is complete or the utility function is exponential.
Nils Detering (Düsseldorf University)
Titel: Pricing options on flow forwards by neural networks in Hilbert space
Abstract: We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as an optimization problem in a Hilbert space of real-valued functions on the positive real line, which is the state space for the term structure dynamics. This optimization problem is solved by facilitating a feedforward neural network architecture designed for approximating continuous functions on the state space. The proposed neural network is built upon the basis of the Hilbert space. We provide case studies that show its numerical efficiency, with superior performance over that of a classical neural network trained on sampling the term structure curves.
This is joint work with Fred Espen Benth (University of Oslo) and Luca Galimberti (King's College London)