Nils Detering
Associate Professor in Mathematical Finance
Undergraduate Diversity, Equity, and Inclusion Officer
Department of Statistics & Applied Probability
University of California, Santa Barbara
Santa Barbara, CA 93106, USA
Email: detering[at]pstat.ucsb.edu
Office: South Hall 5505
Teaching:
- MATH CS 120: Special Topic (Random Graphs and Random Matrices) (Spring 2020)
- MATH CCS 121: Probability and Combinatorics (Spring
2019, Fall 2020, Fall 2021)
- PSTAT 160A: Applied Stochastic Processes (Fall 2018, Winter 2019, Winter 2021, Spring 2022, Fall 2022, Winter 2023)
- PSTAT 170: Introduction to Mathematical Finance
(Winter 2017, Fall 2017, Spring 2018)
- PSTAT 210: Measure Theory for Probability (Fall 2016,
Fall 2017, Fall 2019, Fall 2020)
- PSTAT 213A: Introduction To Probability Theory And Stochastic Processes (Fall 2021, Fall 2022)
- PSTAT 221B: Advanced Probability Theory (Random Graphs and Systemic Risk) (Winter 2017)
- PSTAT 223C: Advanced Topics in Financial Modeling (Systemic Risk) (Spring 2018)
- PSTAT 222B/223B: Advanced Stochastic Processes/Financial Modelling (Winter 2023)
- PSTAT 221C/223C: Advanced Probability Theory/Financial Modelling (Spring 2023)
Research Interests:
My research is in financial mathematics and related questions in probability and data science. My current interests split roughly into three areas:
Financial systemic risk: The financial crisis has shown that one needs to access and manage financial risk not only for individual financial institutions but also for the entire financial system as a whole. The goal is to reduce the likelihood that losses of some banks negatively affect the wider economy, and that, in order to mitigate contagion, costly government intervention and bank bailouts are necessary. I use probabilistic tools, such as random graphs, to analyze default contagion and fire sales in financial systems. I have obtained results that can be used to determine the final state of the system after a local shock propagates, to classify a given financial system as resilient/non-resilient to local shocks, and to determine capital requirements that ensure resilience of the financial system.
Infinite-dimensional stochastic analysis and energy markets: At energy exchanges like NYMEX, CME, EEX and NordPool, one observes forward prices for different delivery maturities. This naturally leads to a curve that describes the current state of the market. Dynamic models are then typically defined based on some stochastic partial differential equation where the solution process takes values in a function space. My contributions in this area cover theoretical work in the area of infinite dimensional stochastic processes and stochastic partial differential equations, and more applied work that directly addresses the pricing and hedging of energy derivatives and calibration methods based on neural networks.
Machine learning for finance: Machine learning has entered financial mathematics in the past few years. However, standard machine learning techniques are often not well suited to attack problems faced in financial mathematics. I am developing universal approximation results for neural networks in Fréchet spaces. These techniques are particularly suitable when dealing with functional data, a situation common in financial markets. I am also working on applications of these results for the pricing of flow derivatives and for PDE based option pricing.
Publications:
- Percolation in Random Graphs of Unbounded Rank, with J. Lin
submitted
- When do you Stop Supporting your Bankrupt Subsidiary? A Systemic Risk Perspective, with M. Bichuch
submitted
- Abstract polynomial processes, with F.E. Benth and P. Krühner
submitted
- Pricing options on flow forwards by neural networks in Hilbert space, with F.E. Benth and L. Galimberti
Finance & Stochastics, accepted
- Reinforcement
Learning Algorithm for Mixed Mean Field Control Games, with A. Angiuli, J.-P. Fouque, and J. Lin
Journal of Machine Learning, accepted
- Neural Networks in Frechet spaces, with F.E. Benth and L. Galimberti
Annals of Mathematics and Artificial Intelligence, accepted
- Reinforcement Learning for Intra-and-Inter-Bank Borrowing and Lending
Mean Field Control Game, with A. Angiuli, J.-P. Fouque,
J. Lin, and M. Laurière
3rd ACM International Conference on AI in Finance (best paper award)
- Stochastic Volterra integral equations and a class of first order stochastic partial differential equations, with F.E. Benth and P. Krühner
Stochastics: An International Journal of Probability and Stochastic
Processes, accepted
- Suffocating Fire Sales, with T. Meyer-Brandis, K. Panagiotou and D. Ritter
SIAM Journal on Financial Mathematics, accepted
- Accuracy of Deep Learning in Calibrating HJM Forward Curves, with F.E. Benth and S. Lavagnini
Digital Finance, 2021
- An Integrated Model for Fire Sales and Default Contagion, with T. Meyer-Brandis, K. Panagiotou and D. Ritter
Mathematics and Financial Economics Volume 15, Page 59-101, 2021
- Financial Contagion in a Stochastic Block Model, with T. Meyer-Brandis, K. Panagiotou and D. Ritter
International Journal of Theoretical and Applied Finance, Vol 23, Issue 08, 2020
- Independent increment processes: A multilinearity preserving property, with F.E. Benth and P. Krühner
Stochastics: An International Journal of Probability and Stochastic
Processes, Pages 1-30, 2020
- Serotonergic axons as Fractional Brownian Motion paths: Insights into the self-organization of regional densities, with S. Janusonis, R. Metzler and T. Vojta
Frontiers In Computational Neuroscience, Volume 14, June, 2020
- Directed Chain Stochastic Differential Equations with J.-P. Fouque and T. Ichiba
Stochastic Processes and their Applications, 130(4), Page
2519-2551, April 2020
- Bootstrap percolation in directed and inhomogeneous random graphs, with T. Meyer-Brandis and K. Panagiotou
Electronic Journal of Combinatorics, 26(2), Page 1-43, 2019
- Managing Default Contagion in Financial Networks, with T. Meyer-Brandis, K. Panagiotou and D. Ritter
SIAM Journal on Financial Mathematics, 10(2), Page 430-465, 2019
- Systemic Risk in Networks , with T. Meyer-Brandis, K. Panagiotou and D. Ritter
Network Science - An Aerial View from Different Perspectives
(Editors: F. Biagini, G. Kauermann, T. Meyer-Brandis), 2019
- Quadratic hedging with multiple assets under illiquidity with applications in energy markets, with C. Christodoulou and T. Meyer-Brandis
International Journal of Theoretical and Applied Finance, Vol. 21, No. 04, 2018
- A stochastic approach to serotonergic fibers in mental disorders, with S. Janusonis
Biochemie, 2018
- The Model Risk of Contingent Claims, with N. Packham
Quantitative Finance, 16:9 , Page 1357-1374, 2016
- Pricing and hedging asian-style options in energy, with F.E. Benth
Finance & Stochastics, Vol. 19(4), Page 849-889, 2015
- Model risk in incomplete markets with jumps, with N. Packham
Springer Proceedings in Mathematics & Statistics, Vol. 99, K. Glau et al: Innovations in Quantitative Risk Management, 2014
- Return distributions of equity-linked retirement plans under jump and interest rate risk, with A. Weber and U. Wystup
European Actuarial Journal Vol. 3(1), Page 203-228, 2013
- Return distributions of equity-linked retirement plans, with A. Weber and U. Wystup
Statistical Tools for Finance and Insurance, 2.Ed., Berlin: Springer, S. 393-413, 2011