Research articles for the 2021-03-07

A deep learning model for gas storage optimization
Nicolas Curin,Michael Kettler,Xi Kleisinger-Yu,Vlatka Komaric,Thomas Krabichler,Josef Teichmann,Hanna Wutte

To the best of our knowledge, the application of deep learning in the field of quantitative risk management is still a relatively recent phenomenon. In this article, we utilize techniques inspired by reinforcement learning in order to optimize the operation plans of underground natural gas storage facilities. We provide a theoretical framework and assess the performance of the proposed method numerically in comparison to a state-of-the-art least-squares Monte-Carlo approach. Due to the inherent intricacy originating from the high-dimensional forward market as well as the numerous constraints and frictions, the optimization exercise can hardly be tackled by means of traditional techniques.

A nonparametric algorithm for optimal stopping based on robust optimization
Bradley Sturt

Optimal stopping is a class of stochastic dynamic optimization problems with applications in finance and operations management. In this paper, we introduce a new method for solving stochastic optimal stopping problems with known probability distributions. First, we use simulation to construct a robust optimization problem that approximates the stochastic optimal stopping problem to any arbitrary accuracy. Second, we characterize the structure of optimal policies for the robust optimization problem, which turn out to be simple and finite-dimensional. Harnessing this characterization, we develop exact and approximation algorithms for solving the robust optimization problem, which in turn yield policies for the stochastic optimal stopping problem. Numerical experiments show that this combination of robust optimization and simulation can find policies that match, and in some cases significantly outperform, those from state-of-the-art algorithms on low-dimensional, non-Markovian optimal stopping problems from options pricing.

Asymptotic Linearity of Consumption Functions and Computational Efficiency
Qingyin Ma,Alexis Akira Toda

We prove that the consumption functions in optimal savings problems are asymptotically linear if the marginal utility is regularly varying. We also analytically characterize the asymptotic marginal propensities to consume (MPCs) out of wealth. Our results are useful for obtaining good initial guesses when numerically computing consumption functions, and provide a theoretical justification for linearly extrapolating consumption functions outside the grid.

Fairness in Credit Scoring: Assessment, Implementation and Profit Implications
Nikita Kozodoi,Johannes Jacob,Stefan Lessmann

The rise of algorithmic decision-making has spawned much research on fair machine learning (ML). Financial institutions use ML for building risk scorecards that support a range of credit-related decisions. Yet, the literature on fair ML in credit scoring is scarce. The paper makes two contributions. First, we provide a systematic overview of algorithmic options for incorporating fairness goals in the ML model development pipeline. In this scope, we also consolidate the space of statistical fairness criteria and examine their adequacy for credit scoring. Second, we perform an empirical study of different fairness processors in a profit-oriented credit scoring setup using seven real-world data sets. The empirical results substantiate the evaluation of fairness measures, identify more and less suitable options to implement fair credit scoring, and clarify the profit-fairness trade-off in lending decisions. Specifically, we find that multiple fairness criteria can be approximately satisfied at once and identify separation as a proper criterion for measuring the fairness of a scorecard. We also find fair in-processors to deliver a good balance between profit and fairness. More generally, we show that algorithmic discrimination can be reduced to a reasonable level at a relatively low cost.

Sector coupling via hydrogen to lower the cost of energy system decarbonization
Guannan He,Dharik S. Mallapragada,Abhishek Bose,Clara F. Heuberger,Emre Gençer

There is growing interest in hydrogen (H$_2$) use for long-duration energy storage in a future electric grid dominated by variable renewable energy (VRE) resources. Modelling the role of H$_2$ as grid-scale energy storage, often referred as "power-to-gas-to-power (P2G2P)" overlooks the cost-sharing and emission benefits from using the deployed H$_2$ production and storage assets to also supply H$_2$ for decarbonizing other end-use sectors where direct electrification may be challenged. Here, we develop a generalized modelling framework for co-optimizing energy infrastructure investment and operation across power and transportation sectors and the supply chains of electricity and H$_2$, while accounting for spatio-temporal variations in energy demand and supply. Applying this sector-coupling framework to the U.S. Northeast under a range of technology cost and carbon price scenarios, we find a greater value of power-to-H$_2$ (P2G) versus P2G2P routes. P2G provides flexible demand response, while the extra cost and efficiency penalties of P2G2P routes make the solution less attractive for grid balancing. The effects of sector-coupling are significant, boosting VRE generation by 12-55% with both increased capacities and reduced curtailments and reducing the total system cost (or levelized costs of energy) by 6-14% under 96% decarbonization scenarios. Both the cost savings and emission reductions from sector coupling increase with H$_2$ demand for other end-uses, more than doubling for a 96% decarbonization scenario as H$_2$ demand quadraples. Moreover, we found that the deployment of carbon capture and storage is more cost-effective in the H$_2$ sector because of the lower cost and higher utilization rate. These findings highlight the importance of using an integrated multi-sector energy system framework with multiple energy vectors in planning energy system decarbonization pathways.

Tail forecasts of inflation using time-varying parameter quantile regressions
Michael Pfarrhofer

This paper proposes methods for Bayesian inference in time-varying parameter (TVP) quantile regression (QR) models. We use data augmentation schemes to facilitate the conditional likelihood, and render the model conditionally Gaussian to develop an efficient Gibbs sampling algorithm. Regularization of the high-dimensional parameter space is achieved via flexible dynamic shrinkage priors. A simple version of the TVP-QR based on an unobserved component (UC) model is applied to dynamically trace the quantiles of the distribution of inflation in the United States (US), the United Kingdom (UK) and the euro area (EA). We conduct an out-of-sample inflation forecasting exercise to assess predictive accuracy of the proposed framework versus several benchmarks using metrics to capture performance in different parts of the distribution. The proposed model is competitive and performs particularly well for higher-order and tail forecasts. We analyze the resulting predictive distributions and find that they are often skewed and feature heavier than normal tails.

The Climate Extended Risk Model (CERM)
Josselin Garnier

This paper is directed to the financial community and focuses on the financial risks associated with climate change. It, specifically, addresses the estimate of climate risk embedded within a bank loan portfolio. During the 21st century, man-made carbon dioxide emissions in the atmosphere will raise global temperatures, resulting in severe and unpredictable physical damage across the globe. Another uncertainty associated with climate, known as the energy transition risk, comes from the unpredictable pace of political and legal actions to limit its impact. The Climate Extended Risk Model (CERM) adapts well known credit risk models. It proposes a method to calculate incremental credit losses on a loan portfolio that are rooted into physical and transition risks. The document provides detailed description of the model hypothesis and steps. This work was initiated by the association Green RWA (Risk Weighted Assets). It was written in collaboration with Jean-Baptiste Gaudemet, Anne Gruz, and Olivier Vinciguerra (, who contributed their financial and risk expertise, taking care of its application to a pilot-portfolio. It extends the model proposed in a first white paper published by Green RWA (

The Golden Age of the Mathematical Finance
José Manuel Corcuera

This paper is devoted to show that the last quarter of the past century can be considered as the golden age of the Mathematical Finance. In this period the collaboration of great economists and the best generation of probabilists, most of them from the Strasbourg's School led by Paul Andr\'e Meyer, gave rise to the foundations of this discipline. They established the two fundamentals theorems of arbitrage theory, close formulas for options, the main modelling a

Time-inconsistent consumption-investment problems in incomplete markets under general discount functions
Yushi Hamaguchi

In this paper, we study a time-inconsistent consumption-investment problem with random endowments in a possibly incomplete market under general discount functions. We provide a necessary condition and a verification theorem for an open-loop equilibrium consumption-investment pair in terms of a coupled forward-backward stochastic differential equation. Moreover, we prove the uniqueness of the open-loop equilibrium pair by showing that the original time-inconsistent problem is equivalent to an associated time-consistent one.