List of Publications
Research History until Present, Listed in zbMATH (including all papers which I re-reviewed (for zbMATH))
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My Work in arXiv until Present
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My Research Profile in ORCID
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Monographs
- Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP
Functions; [arXiv version] and its updated version, taking into account important comments and remarks of the referees, the inclusion of a brand-new paper of J.-L. Krivine himself and an implied supplementary consideration - Proposition 6.2.5 (will be published as volume 2349 of the Lecture Notes in Mathematics series around August 2024)
- Restructuring counterparty credit risk (joint work with Claudio Albanese and Damiano Brigo); Discussion Paper, Deutsche Bundesbank, No 14/2013 [PDF]
Recent Preprints (uploaded to arXiv)
Publications (in peer-reviewed journals)
- An analysis of the Rüschendorf transform - with a view towards Sklar's Theorem; Depend. Model., Vol. 3, No. 1, 113–125 [http://dx.doi.org/10.1515/demo-2015-0008]
- Restructuring counterparty credit risk (joint work with Claudio Albanese and Damiano Brigo); International Journal of Theoretical and Applied Finance (IJTAF), Vol. 16, No. 2 (2013), 1350010 [29 pages], [Abstract]
- Geometry of polar wedges in Riesz spaces and super-replication prices in incomplete financial markets (joint work with Mark P. Owen); Positivity, Vol. 13, No. 1 (2009), 201-224 (Review A, Review B) [PDF]
- Some open problems in the geometry of operator ideals; Positivity, Vol. 13, No. 1 (2009), 300-304
[PDF]
- On utility-based superreplication prices of contingent claims with unbounded payoffs (joint work with Mark P. Owen), J. Appl. Probab., Vol. 44, No. 4 (2007), 880-888 (Review) [PDF]
- The numeraire portfolio in financial markets modeled by a multi-dimensional jump diffusion process (joint work with Ralf Korn and Manfred Schäl), Decisions in Economics and Finance 26, No. 2 (2003), 153-166 (Review) [PDF]
- On normed products of operator ideals which contain $\frak{L}_2$ as a factor, Arch. Math. 80 (2003), 61-70 (Review A, Review B) [PDF]
- Extension of finite rank operators and operator ideals with the property (I), Math. Nachr. 238 (2002), 144-159 (Review A, Review B) [PDF]
- Local properties of accessible injective operator ideals, Czech.
Math. J., Vol. 47, No. 1 (1998), 119-133 (Review A, Review B) [PDF]
- Operators with extension property and the principle of local reflexivity, Acta Univ. Carolin. Math. Phys. 37, No. 2 (1996), 55-63 (Review A, Review B) [PDF]
- Compositions of operator ideals and their regular hulls, Acta Univ. Carolin. Math. Phys. 36, No. 2 (1995), 69-72 (Review A, Review B) [PDF]
- Operator ideals and the principle of local reflexivity, Acta Univ. Carolin. Math. Phys. 33, No. 2 (1992), 115-120 (Review A, Review B) [PDF]
- Conjugated Operator Ideals and the A-Local Reflexivity Principle, Preprint Nr. 210, Universität Kaiserslautern (contains unpublished parts*) (1991) [PDF]
* There is a little story about this preprint (my first one) that should be mentioned here regarding a better understanding of its non-published parts. When I namely presented my first results in a PhD
seminar on functional analysis in Kaiserslautern, my supervisor Professor E. Schock warned me that I would have taken a quite risky path now. He namely knew about
two colleagues in Oldenburg who would even be preparing a whole book on the same topic (namely that one here: Tensor Norms and Operator Ideals)! I am still deeply grateful to him for having informed me on this crucial issue. Only thanks to his attention, I could secure all of my results - which I discovered independently from the research team in Oldenburg, yet approximately at the same time
(what happens rather often in mathematical research - and actually happened to me again in 2000). Consequently, Professor A. Defant, one of the authors of Tensor Norms and Operator Ideals became my second PhD supervisor! Proposition 1.4 on p. 5, together with Lemma 1.5 on p. 6 and Theorem 1.6 on p. 7 reflects the consistency of the language in Tensor Norms and Operator Ideals and my own, independently coined symbolic notation. Every interested reader should please overlook my somewhat unusual English in some places at that time.
Selected Slides and Lecture Notes
- Completely correlation preserving mappings: a way to tackle the upper bound of the real
and complex Grothendieck constant? [PDF]
- Mathematical Modelling of Infectious Diseases for Public Health England (slides 12, 13 slightly updated in view of the exponential expansion of the COVID-19 pandemics) [PDF] - regarding explanation cf. also "Oxford Mathematician explains SIR disease model for COVID-19 (Coronavirus)", the Helmholtz working paper Stellungnahme der Helmholtz-Initiative "Systemische Epidemiologische Analyse der COVID-19-Epidemie" and Mathematik der Kontaktreduktion
- A statistical interpretation of Grothendieck's inequality: towards an approximation of the real Grothendieck constant [PDF]
- Outlining the Pricing of Cliquet-style Options:
From Crude Monte Carlo Simulation to Statistical Machine Learning (Implemented in
Python (v3.6.5))[PDF]
- "A statistical interpretation of Grothendieck's inequality and its relation to the size of non-locality of quantum mechanics" (a video of my talk, presented at the Workshop on Combining Viewpoints in Quantum Theory at the ICMS in Edinburgh, 19-22 March 2018)
- A statistical interpretation of Grothendieck's inequality and its relation to the size of non-locality of quantum mechanics (important correction on the last slide!) [PDF]
- Towards a Quantification of Model Risk in Derivatives Pricing [PDF]
- Sklar's Theorem and the Rüschendorf transform revisited - An analysis of right quantiles [PDF]
- A few remarks on the pricing of contingent convertibles [PDF]
- Random jump measures: addendum [PDF]
- On a result of G. Pisier in the theory of operator spaces (updated and slightly extended) [PDF]
- Operator ideals and approximation properties
of Banach spaces [PDF]
- Approximation properties of Banach spaces, the principle of local reflexivity for operator ideals, and factorisation of operators with finite rank [PDF]
- Stochastic Modelling of Counterparty Credit Risk, CVA and DVA – with a Glimpse at the New Regulatory Framework Basel III [PDF]
- "Bilateral first-to-default CVA and Basel III-CVA risk charges embedded in the context of an integrated portfolio risk model - First thoughts (Non-Confidential Version)" (my own talk presented at the 2011 BCBS-RTF meeting in Istanbul, its first improved version at University of Southampton and its following update)
- A Crash Course on Brownian Motion, Continuous Martingales and Itô Calculus [PDF]
- Geometry of polar cones and superreplication prices in incomplete financial markets [DVI, PDF]
- The stochastic logarithm of semimartingales and market prices of risk [DVI, PDF]
- A Hilbert space approach to Wiener Chaos Decomposition and its applications to finance [DVI, PDF]
Well, does the following paper contain plagiarism? I am talking about p.31 - p.37 + Remark 3.2.11.-1. of The Malliavin Calculus. At least Han Zhang's choice of notation and construction appear to be the same, but (s)he did not refer to my original work which had been (firstly) finished in 2003. This could be confirmed by Sergio Albeverio from University of Bonn who read the first draft carefully. As proof, please check also the footnote on p. 3 of the following paper of Farshid Jamshidian: On the combinatorics of iterated stochastic integrals !
- A first approach to randomness in financial markets with a view towards option pricing [PDF]
- Das Markowitz-Modell zur Bestimmung optimaler Aktienportfolios (German Version) [DVI, PDF]
Thesis ("Promotionsschrift")
- Konjugierte Operatorenideale und das $\scr{A}$-lokale
Reflexivitätsprinzip (Conjugate operator ideals and the $\scr{A}$-local
reflexivity principle ), University of Kaiserslautern (1991) (Review)
Thesis ("Diplomarbeit")
- Multilineare Funktionalideale (Ideals of multilinear functionals),
University of Kaiserslautern (1986)
Other Scholarly Activities
- Proofreading of: DIESTEL, J., JARCHOW H., PIETSCH A.: OPERATOR IDEALS,
Jenaer Schriften zur Mathematik und Informatik (Math/Inf/99/19),
Friedrich-Schiller Universität Jena
- Assistant Editor of the journal
FINANCE AND STOCHASTICS (October
1997 - March 2000)
- Proofreading of chapter 3 in: EMBRECHTS,
P., KLÜPPELBERG, C., T. MIKOSCH: MODELLING EXTREMAL EVENTS, Springer
(1997)
- Proposition 25.4.1 in: DEFANT, A., K. FLORET: TENSOR NORMS AND OPERATOR
IDEALS , North-Holland Amsterdam, London, New York, Tokio (1993)
TeX-trickery :-)
It seems to me that the current TeX environment does not include the often used symbol for the indicator function (a close ''double one''). However, the following definitions should produce the required symbol in a satisfactory manner (for slides and articles, respectively):
- \newcommand{\ind}{1\hspace{-NUMBERmm}{1}}.
Here, NUMBER should be contained in the interval [3.0, 3.2] if the symbol should appear on a slide.
- \newcommand{\ind}{1\hspace{-NUMBERmm}{1}}.
Here, NUMBER = 2.5 (resp. NUMBER = 2.3) if the symbol should appear on a standard LaTeX 2e (resp. AMS-TeX) document.
Here is something else which might be of interest for all those of you who also prefer to work efficiently lazy and who also like to work with suggestive symbolic notation instead. One such example is the nice symbol which describes a disjoint union of sets. Most of you know that disjoint unions are indicated by a little dot which sits in the middle of the standard \bigcup symbol. Well, also such a symbol seems not to exist in the current TeX environment? If you know a source, please send me a message (I coudn't find it in CTAN...)! Of course, there exists an alternative to the dot, coded as \biguplus. However, I do not like to be reminded at funerals, being forced to look at the big cross sitting in the middle of the \bigcup symbol... :-)
Anyway, if the required symbol should appear on a standard LaTeX 2e (resp. AMS-TeX) document, a simple shift of the dot to the center of \biguplus, together with an annexation of the necessary space(!) for the following symbol, directly leads to the following three possible solutions (a general one and two more specific ones):
- \newcommand\dju[4]{\bigcup_{#1}^{#2}\hspace{-#3mm\cdot}\hspace{#4mm}}.
That new command is the general version. It allows to shift the dot manually, indicated by the positive variables #3 and #4 (observe the minus sign(!)). This might be necessary, dependent on your chosen index set notation or your chosen text environment.
Examples: "Let $A = \dju{n=1}{\infty}{9}{7} A_n$ and..." resp. "Let $G = \dju{\alpha \in A}{}{9.5}{9} G_\alpha$ and ...".
However, if you are in an equation environment, you can directly use the following solution (given the case, that you are considering countable unions):
- \newcommand\cdju[2]{\bigcup_{#1}^{#2}\hspace{-4.2mm\cdot}\hspace{2.2mm}}.
Example: "Let
\[
A = \cdju{n=1}\infty A_n
\]
and ...".
Well, if you are working here within a text line only, then you can use the following one:
- \newcommand\ldju[2]{\bigcup_{#1}^{#2}\hspace{-9mm\cdot}\hspace{7mm}}.
Example: "Let $A = \ldju{n=1}\infty A_n$ and ...".
The abbreviation "dju" is my lazy version of the word "disjoint union", "c" simply stands for "centered" and "l" stands for "lined". If that's too short, you can change the respective names, of course... :-)
Current Version: February 23, 2024