Nils Detering

N Detering

Associate Professor in Mathematical Finance

Undergraduate Advisor for Financial Mathematics and Actuarial Science
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
Office Hours Undergraduate Advising: Monday 5:00-6:00 pm

My CV

Teaching (UCSB only):

Research Interests:

My research is in financial mathematics and related questions in probability. 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:

  1. Reinforcement Learning Algorithm for Mixed Mean Field Control Games, with A. Angiuli, J.-P. Fouque, and J. Lin
    submitted
  2. Pricing options on flow forwards by neural networks in Hilbert space, with F.E. Benth and L. Galimberti
    submitted
  3. When do you Stop Supporting your Bankrupt Subsidiary?, with M. Bichuch
    submitted
  4. Neural Networks in Frechet spaces, with F.E. Benth and L. Galimberti
    submitted
  5. Abstract polynomial processes, with F.E. Benth and P. Krühner
    submitted
  6. 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
  7. Suffocating Fire Sales, with T. Meyer-Brandis, K. Panagiotou and D. Ritter
    SIAM Journal on Financial Mathematics, accepted
  8. Accuracy of Deep Learning in Calibrating HJM Forward Curves, with F.E. Benth and S. Lavagnini
    Digital Finance, 2021
  9. 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
  10. 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
  11. 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
  12. 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
  13. Directed Chain Stochastic Differential Equations with J.-P. Fouque and T. Ichiba
    Stochastic Processes and their Applications, 130(4), Page 2519-2551, April 2020
  14. 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
  15. 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
  16. 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
  17. 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
  18. A stochastic approach to serotonergic fibers in mental disorders, with S. Janusonis
    Biochemie, 2018
  19. The Model Risk of Contingent Claims, with N. Packham
    Quantitative Finance, 16:9 , Page 1357-1374, 2016
  20. Pricing and hedging asian-style options in energy, with F.E. Benth
    Finance & Stochastics, Vol. 19(4), Page 849-889, 2015
  21. 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
  22. 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
  23. 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