List of Publications
Publications (in peerreviewed 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/demo20150008]
 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 superreplication prices in incomplete financial markets (joint work with Mark P. Owen); Positivity, Vol. 13, No. 1 (2009), 201224 (Review A, Review B) [PDF]
 Some open problems in the geometry of operator ideals; Positivity, Vol. 13, No. 1 (2009), 300304
[PDF]
 On utilitybased superreplication prices of contingent claims with unbounded payoffs (joint work with Mark P. Owen), J. Appl. Probab., Vol. 44, No. 4 (2007), 880888 (Review) [PDF]
 The numeraire portfolio in financial markets modeled by a multidimensional jump diffusion process (joint work with Ralf Korn and Manfred Schäl), Decisions in Economics and Finance 26, No. 2 (2003), 153166 (Review) [PDF]
 On normed products of operator ideals which contain $\frak{L}_2$ as a factor, Arch. Math. 80 (2003), 6170 (Review A, Review B) [PDF]
 Extension of finite rank operators and operator ideals with the property (I), Math. Nachr. 238 (2002), 144159 (Review A, Review B) [PDF]
 Local properties of accessible injective operator ideals, Czech.
Math. J., Vol. 47, No. 1 (1998), 119133 (Review A, Review B) [PDF]
 Operators with extension property and the principle of local reflexivity, Acta Univ. Carolin. Math. Phys. 37, No. 2 (1996), 5563 (Review A, Review B) [PDF]
 Compositions of operator ideals and their regular hulls, Acta Univ. Carolin. Math. Phys. 36, No. 2 (1995), 6972 (Review A, Review B) [PDF]
 Operator ideals and the principle of local reflexivity, Acta Univ. Carolin. Math. Phys. 33, No. 2 (1992), 115120 (Review A, Review B) [PDF]
Monographs
 Restructuring counterparty credit risk (joint work with Claudio Albanese and Damiano Brigo); Discussion Paper, Deutsche Bundesbank, No 14/2013 [PDF]
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 Covid19 infection) [PDF]  regarding explanation cf. also "Oxford Mathematician explains SIR disease model for COVID19 (Coronavirus)" and the Helmholtz working paper Stellungnahme der HelmholtzInitiative "Systemische Epidemiologische Analyse der COVID19Epidemie"
 A statistical interpretation of Grothendieck's inequality: towards an approximation of the real Grothendieck constant [PDF]
 Outlining the Pricing of Cliquetstyle 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 nonlocality of quantum mechanics" (a video of my talk, presented at the Workshop on Combining Viewpoints in Quantum Theory at the ICMS in Edinburgh, 1922 March 2018)
 A statistical interpretation of Grothendieck's inequality and its relation to the size of nonlocality 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 firsttodefault CVA and Basel IIICVA risk charges embedded in the context of an integrated portfolio risk model  First thoughts (NonConfidential Version)" (my own talk presented at the 2011 BCBSRTF 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 MarkowitzModell zur Bestimmung optimaler Aktienportfolios (German Version) [DVI, PDF]
My Work in arXiv (as Author and as CoAuthor)

Currently, when our time allows it, we are heavily thinking about a highly fascinating and beautiful open problem which surprisingly links both, pure mathematics and applied mathematics (if such a separation within mathematics can be made at all) and shows deep applications to the foundations of quantum theory and quantum computing and even large data analysis.
More precisely, our approach needs a strong inclusion and interplay of linear algebra, matrix analysis, real and complex analysis, some harmonic analysis, theory and applications of special functions including Hermite functions, integer programming with Booleanvalued functions, convex optimisation including semidefinite programming, probability theory, stochastic analysis, and even some statistics including dependence modelling with copulas (using techniques, wellknown to the Second Line of Defence in the financial industry) and computational complexity theory (implying a curse of dimensionality; also due to highdimensional integration over finitedimensional spheres!). It seems that all that won't suffice. It appears to us that in fact some new mathematics has to be developed  to shed further light on the convex set of all correlation matrices and certain nonlinear mappings between its elements.
That nice problem is the determination of the exact value of the real and complex Grothendieck constant in Grothendieck's famous inequality.
It seems that again we only see a tip of an iceberg here and that even an approximation of the real and complex Grothendieck constant already requires a persistent banging of our head against very massively constructed entrance doors...
Nevertheless, we hope that in the next months our first publishable paper on this topic will be ready for the arXiv. At least also our approach immediately reproduces Krivine's constant as an upper bound of the real Grothendieck constant as a particular case and shows us a possible path how to obtain a smaller value than Krivine's constant  following parts of this highly fascinating, yet technically quite demanding paper.
Moreover, based on our approach we will provide a further proof of Grothendieck's inequality which in addition just needs an understanding of the behaviour of two correlated onedimensional standard normally distributed random variables. However, the so obtained constant exceeds Krivine's constant a slightly bit, and it seems that this approach (by making use of correlated normally distributed random variables) cannot be used to obtain another explicit value for the real Grothendieck constant which is strictly below Krivine's value.
 Direct link
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),
FriedrichSchiller 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 , NorthHolland Amsterdam, London, New York, Tokio (1993)
TeXtrickery :)
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. AMSTeX) 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. AMSTeX) 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: April 21, 2020