List of Publications
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]
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
- 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]
My Work in arXiv (as Author and as Co-Author)
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: January 30, 2018