Research Interests

Primary Interests (including publications in peer-reviewed journals)

• Abstract Analysis
  • Geometry of Banach spaces
  • Operator algebras
  • Non-commutative functional analysis
  • Operator spaces and quantum information

• Operator Theory
  • Operator ideals and tensor norms
  • Factorization of linear operators
  • The principle of local reflexivity for operator ideals

• Measure Theory and Stochastic Analysis
  • Martingale theory
  • Stochastic integration
  • Malliavin calculus
  • Vector measures and POVMs

• Mathematical Foundations of Financial Analysis
  • Mathematical finance
  • Pricing and hedging of contingent claims
  • Incomplete markets (including Lévy processes and non-continuous semimartingales in general, utility maximisation)
  • Application of functional analytic and convex analytic methods to problems of mathematical finance
  • Approximation problems in financial modeling
  • Financial risk measurement (risk measures, credit risk modelling, CCR, CVA, DVA, enhancements of Basel III)

Membership in Research Networks

• ResearchGate

Refereeing Activities

• Reviewer for zbMath -> [Login]

• Referee for
  • Economic Notes
  • Elemente der Mathematik
  • Finance and Stochastics
  • Quantitative Finance
  • Mathematical Finance
  • Risk Magazine (Cutting Edge)

Online Databases for Mathematical Research

• Zentralblatt MATH Database zbMath

• MathSciNet

• arXiv

• Séminaire de probabilités de Strasbourg

• Table of contents for issues of Annales de l'Institut Henri Poincaré. Nouvelle série. Section B. Calcul des Probabilités et Statistique

Further Interests

• Foundations of Mathematical Physics
  • Philosophical interpretation of quantum mechanics
  • Mathematical structures in quantum probability and quantum information theory (QIT)
  • Mathematical structures in quantum field theory (QFT)
  • SR, GRT
  • Time, information and entropy
  • A link between general relativity and finance

• Differential Geometry
• Number Theory
• Cryptology (i.e., Cryptography and Cryptoanalysis)
[Many thanks to Peter Wagner for pointing this highly fascinating subject out to me!]