Machine Learning (ML) provides techniques for universal function approximation. In this talk, we apply such techniques to the acceleration of complex derivatives pricing, focusing on Value-at- Risk computations for Bermudan interest rate options. We introduce different applicable ML methods, and we present results from our client projects. Moreover, we propose ways to address regulatory requirements via the model lifecycle process.

A constant weight asset allocation is a popular investment strategy and is optimal under a suitable continuous model. We study the tracking error for the target continuous rebalancing by a feasible finite-time rebalanc- ing under a general multi-dimensional Brownian semimartingale model of asset prices. In a high-frequency asymptotic framework, we derive an asymptotically efficient strategy among simple predictable processes.

Quantum observables determine for instance the stress tensor and heat flux in fluid dynamics. In the talk I will show which properties are used for approximating such quantum observables by classical molecular dynamics and what is new when mean-field molecular dynamics improves the classical setting, using features of the Gibbs distribution.

We study the optimal investment-consumption problem for an agent whose preferences are governed by Epstein–Zin stochastic differential utility and who invests in a constant-parameter Black–Scholes– Merton market. We assume that purchases and sales of the risky asset are subject to proportional transaction costs. We fully characterise all parameter combinations for which the problem is well posed (which may depend on the level of transaction costs). We also provide a full verification argument that relies on no additional technical assumptions and uses primary methods only. Even in the special case of power utility, our arguments are significantly simpler and more elegant than the results in the extant literature. A novel key idea is to parametrise consumption and the value function in terms of the shadow fraction of wealth. The talk is based on joint work with David Hobson and Alex Tse.

Conference webpage

Stochastic portfolio theory is a framework to study large equity markets over long time horizons. In such settings investors are often confined to trading in an “open market” setup consisting of only assets with high capitalizations. In this work we relax previously studied notions of open markets and develop a tractable framework for them under mild structural conditions on the market. Within this framework we also introduce a large parametric class of processes, which we call rank Jacobi processes. They produce a stable capital distribution curve consistent with empirical observations. Moreover, there are explicit expressions for the growth-optimal portfolio, and they are also shown to serve as worst-case models for a robust asymptotic growth problem under model ambiguity. Lastly, the rank Jacobi models are shown to be stable with respect to the total number of stocks in the market. Time permitting, we will show that, under suitable assumptions on the parameters, the capital distribution curves converge to a limiting quantity as the size of the market tends to infinity. This convergence result provides a theoretical explanation for an important empirically observed phenomenon.

This talk is based on joint work with Martin Larsson.

Thermal storage facilities help to mitigate and to manage temporal fluctuations of heat supply and demand for heating and cooling systems of single buildings as well as for district heating systems. We focus on a heating system equipped with several heat production units using also renewable energies and an underground thermal storage. The thermal energy is stored by raising the temperature of the soil inside that storage. It is charged and discharged via heat exchanger pipes filled with a moving fluid.

Besides the numerous technical challenges and the computation of the spatio-temporal temperature dis- tribution in the storage also economic issues such as the cost-optimal control and management of such systems play a central role. The latter leads to challenging mathematical optimization problems. There we incorporate uncertainties about randomly fluctuating renewable heat production, environmental conditions driving the heat demand and supply.

The dynamics of the controlled state process is governed by a PDE, a random ODE, and SDEs modeling energy prices and the difference between supply and demand. Model reduction techniques are adopted to cope with the PDE describing the spatio-temporal temperature distribution in the geothermal storage. Finally, time- discretization leads to a Markov decision process for which we apply numerical methods to determine a cost-optimal control.

This is joint work with Paul Honore Takam (BTU Cottbus-Senftenberg) and Olivier Menoukeu Pamen (AIMS Ghana, University of Liverpool).

In this talk we present a novel deep learning methodology to detect financial asset bubbles by using observed call option prices. We start with an introduction to deep learning and asset price bubbles. We then examine the pitfalls of a naive approach for deep learning-based bubble detection and subsequently introduce our method. We provide theoretical foundations for the method in the context of local volatility models and show numerical results from experiments both on simulated and market data.

The talk is based on joint work with Francesca Biagini, Andrea Mazzon and Thilo Meyer-Brandis.