Preprints
Publications
- A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions
(with
Arnulf Jentzen,
Adrian Riekert and
Florian Rossmannek)
arXiv Preprint 2102.09924
Forthcoming in Journal of Complexity
- Deep splitting method for parabolic PDEs
(with
Christian Beck,
Sebastian Becker,
Arnulf Jentzen and
Ariel Neufeld )
arXiv Preprint 1907.03452
SIAM Journal on Scientific Computing
43(5), 2021, p. A3135–A3154
- Representation of increasing convex functionals with countably additive measures
(with
Michael Kupper and
Ludovic Tangpi)
arXiv Preprint 1502.05763
Studia Mathematica
260, 2021, p. 121–140
- Efficient approximation of high-dimensional functions with neural networks
(with
Arnulf Jentzen and
Florian Rossmannek)
arXiv Preprint 1912.04310
Forthcoming in IEEE
Transactions on Neural Networks and Learning Systems
- Non-convergence of stochastic gradient descent in the training of deep neural networks
(with
Arnulf Jentzen and
Florian Rossmannek)
arXiv Preprint 2006.07075
Journal of Complexity
64, June 2021
- On non-local ergodic Jacobi semigroups: spectral theory, convergence-to-equilibrium and contractivity
(with
Pierre Patie,
Anna Srapionyan and
Aditya Vaidyanathan)
arXiv Preprint 1905.07832
Journal de l'Ecole
Polytechnique – Mathématiques 8, 2021, p. 331–378
- Solving high-dimensional optimal stopping problems using deep learning
(with
Sebastian Becker,
Arnulf Jentzen and
Timo Welti)
arXiv Preprint 1908.01602
European Journal of Applied Mathematics
32(3), 2021, p. 470–514
- Pricing and hedging American-style options with deep learning
(with
Sebastian Becker and
Arnulf Jentzen)
arXiv Preprint 1912.11060
Journal of Risk and Financial Management
13(7), 158, 2020, p. 1–12
- Assessing asset-liability risk with neural networks
(with John Ery and
Mario Wüthrich)
arXiv Preprint 2105.12432
Risks 8(1), 16, 2020, p. 1–17
- Martingale optimal transport duality
(with
Matti Kiiski,
David Prömel and
Mete Soner)
arXiv Preprint 1904.04644
Mathematische Annalen 2020
- Deep optimal stopping
(with
Sebastian Becker and
Arnulf Jentzen)
arXiv Preprint 1804.05394
Journal of Machine Learning Research 20(74), 2019, p. 1–25
- Measuring and allocating systemic risk
(with Markus Brunnermeier)
SSRN Preprint
Risks 7(2), 46, 2019, p. 1–19
- Robust expected utility maximization with medial limits
(with Daniel Bartl and
Michael Kupper)
arXiv Preprint 1712.07699
Journal of
Mathematical Analysis and Applications 471(1–2), 2019, p. 752–775
- Duality formulas for robust pricing and hedging in discrete time
(with
Michael Kupper and
Ludovic Tangpi)
arXiv Preprint 1602.06177
SIAM Journal on Financial Mathematics
8(1), 2017, p. 738–765
- BSEs, BSDEs and fixed point problems
(with Kihun Nam)
arXiv Preprint 1410.1247
Annals of Probability
45(6), 2017, p. 3795–3828
- Duality for increasing convex functionals with countably many marginal constraints
(with Daniel Bartl,
Michael Kupper and
Ludovic Tangpi)
arXiv Preprint 1509.08988
Banach Journal of Mathematical Analysis
11(1), 2017, p. 72–89
- Equilibrium pricing in incomplete markets under translation invariant preferences
(with Ulrich Horst,
Michael Kupper,
Traian Pirvu)
SSRN Preprint
Mathematics of Operations Research
41(1), 2016, p. 174–195
- Multidimensional quadratic and subquadratic BSDEs with special structure
(with Kihun Nam)
arXiv Preprint 1309.6716
Stochastics
87(5), 2015, p. 871–884
- Conditional Analysis on ℝ^{d}
(with Michael Kupper,
Nicolas Vogelpoth)
arXiv Preprint 1211.0747
Set Optimization and Applications – The State of the Art. 2015, p. 179–212
- A reduced form CoCo model with deterministic conversion intensity
(with Zhikai Xu)
SSRN Preprint
The Journal of Risk 17(3), 2015, p. 1–18
- Optimal trade execution under stochastic volatility and liquidity
(with Tardu Sepin)
SSRN Preprint
Applied Mathematical Finance 21(4), 2014, p. 342–362
- BSDEs with terminal conditions that have bounded Malliavin derivative
(with Kihun Nam)
arXiv Preprint 1309.6716
Journal of Functional Analysis 266(3), 2014, p. 1257–1285
- Controlling portfolio skewness and kurtosis
without directly optimizing third and fourth moments
(with Frank Fabozzi,
Charles Fox,
Woo Chang Kim)
PDF
Economic Letters 122(2), 2014, p. 154–158
- How to value a coco
(with Zhikai Xu)
PDF
Creditflux Newsletter October 4, 2013
- Reward-risk ratios
(with Eduard Kromer)
SSRN Preprint
Journal of Investment Strategies 3(1), 2013, p. 1–16
- Weak closedness of monotone sets of lotteries and robust representation of risk preferences
(with Samuel Drapeau,
Michael Kupper)
PDF
Risk Measures and Attitudes. European Actuarial Academy Series
2013, p. 3–9
- BSΔEs and BSDEs with non-Lipschitz drivers:
comparison, convergence and robustness
(with Mitja Stadje)
PDF
Bernoulli 19(3), 2013, p. 1047–1085
- Existence, minimality and approximation of solutions to BSDEs with convex drivers
(with Mitja Stadje)
PDF
Stochastic
Processes and their Applications 122(4), 2012, p. 1540–1565
- Pricing and hedging in affine models with possibility of default
(with Alexander Wugalter)
PDF
SIAM Journal on Financial Mathematics 3(1), 2012, p. 328–350
- Processes of class Sigma, last passage times and drawdowns
(with Ashkan Nikeghbali
and Eckhard Platen)
PDF
SIAM Journal on Financial Mathematics 3(1), 2012, p. 208–303
- Ordered contribution allocations: theoretical properties and applications
(with Eduard Kromer)
PDF
The Journal of Risk 14(1), 2011
- Optimal consumption and investment in incomplete markets with general constraints
(with Ying Hu)
arXiv Preprint 1010.0080
Stochastics and Dynamics
11(2), 2011, p. 283–299
- Composition of time-consistent dynamic monetary risk measures in discrete time
(with Michael Kupper)
PDF
International
Journal of Theoretical and Applied Finance 14(1), 2011, p. 137–162
- A note on the Dai–Singleton canonical representation of
affine term structure models
(with Damir
Filipovic and Bob Kimmel)
PDF
Mathematical Finance
20(3), 2010, p. 509–519
- Recursiveness of indifference prices and translation-invariant preferences
(with Michael Kupper)
PDF
Mathematics and Financial Economics,
2(3), 2009, p. 173–188
- Time-inconsistency of VaR and time-consistent alternatives
(with Mitja Stadje)
PDF
Finance
Research Letters, 6(1), 2009, p. 40–46
- Dual characterization of properties of risk measures on Orlicz hearts
(with Tianhui Michael Li)
PDF
Mathematics and Financial
Economics 2(1), 2008, p. 29–55
- Risk measures on Orlicz hearts
(with Tianhui Michael Li) PDF
(more general version of an earlier paper called
Monetary risk measures on maximal subspaces of Orlicz classes)
Mathematical Finance
19(2), 2009, p. 189–214
- Second order backward stochastic differential
equations and fully non-linear parabolic PDEs
(with H. Mete Soner,
Nizar
Touzi and Nicolas
Victoir)
PDF
Communications
on Pure and Applied Mathematics 60(7), 2007, p. 1081–1110
- Market price of risk specifications for affine
models: theory and evidence
(with Damir
Filipovic
and Bob Kimmel)
PDF
Journal
of Financial Economics 83(1), 2007, p. 123–170
- Dynamic monetary risk measures for bounded
discrete-time processes
(with Freddy Delbaen
and Michael Kupper)
PDF
Electronic Journal
of Probability, 11, 2006, p. 57–106
- Coherent and convex monetary risk measures for
unbounded càdlàg processes
(with Freddy Delbaen
and Michael Kupper)
PDF
Finance
and Stochastics, 10(3), 2006, p. 427–448
- Utility maximization under increasing risk aversion
in one-period models
(with Christopher Summer)
PDF
Finance
and Stochastics, 10(1), 2006, p. 147–158
- Equivalent and absolutely continuous measure changes
for jump-diffusion processes
(with Damir Filipovic and Marc Yor)
PDF
Annals
of Applied Probability, 15(3), 2005, p. 1713–1732
- The multi-dimensional super-replication problem under gamma constraints
(with H. Mete Soner and Nizar
Touzi) PDF
Annales
de l'Institute Henri Poincaré (C) Non Linear Analysis,
22(5), 2005, p. 633–666
- Small time path behavior of double stochastic
integrals and applications to stochastic control
(with H. Mete Soner and Nizar
Touzi) PDF
Annals
of Applied Probability, 15(4), 2005, p. 2472–2495
- Stochastic integral of divergence type with respect
to fractional Brownian motion with Hurst parameter H in
(0,1/2)
(with David Nualart) PDF
Annales
de l'Institute Henri Poincaré (B) Probability and
Statistics, 41(6), 2005, p. 1049–1081
- Coherent and convex monetary risk measures for bounded
càdlàg processes
(with Freddy Delbaen and Michael Kupper) PDF
Stochastic
Processes and their Applications, 112(1), 2004, p. 1–22
- Gaussian moving averages, semimartingales and option
pricing PDF
Stochastic
Processes and their Applications, 109(1), 2003, p. 47–68
- Fractional Ornstein–Uhlenbeck processes
(with Hideyuki Kawaguchi and Makoto
Maejima) PDF
Electronic Journal
of Probability, 8(3), 2003, p. 1–14
- Arbitrage in fractional Brownian motion
models PDF
Finance
and Stochastics, 7(4), 2003, p. 533–553
- Representations of Gaussian measures that are
equivalent to Wiener measure
PDF
Séminaire de Probabilités , Vol. XXXVII, 2003,
p. 81-89. Springer
Lecture Notes in Mathematics, Vol. 1832
- Sensitivity of the Black–Scholes option price to the
local path behavior of the stochastic process modeling the
underlying asset PDF
Proceedings of the Steklov Institute of Mathematics, Vol. 237, 2002, p. 225–239
- Mixed fractional Brownian motion PDF
Bernoulli, 7(6), 2001, p. 913–934
- Regularizing fractional Brownian motion with a view
towards stock price modelling PDF
Diss. ETH No. 14051, 2001