Research interests : Actuarial Science and Finance, Probability and Statistics, Number Theory, Algebra
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Some highlights of my scientific contributions
Number Theory and Algebra
[1] Thesis supervisor (M.-A. Knus) and cosupervisor (U. Stammbach)
[2] From Pythagoras/Fermat to Catalan/Sierpinski
[3] Algebraic tori, Brauer group, cohomology, Hasse principle
[4] Hilbert theorem 90/generalizations
[5] Invariant theory
[6] Golden ratio in insurance pricing
[7] Miscellaneous
Probability and Statistics
[1] Copulas : bivariate extreme value copula, linear Spearman and multidimensional Fréchet copulas, etc.
[2] Dependence measures : Hutchinson-Lai conjecture between Kendall's tau and Spearman's rho, etc.
[3] Stochastic orders : higher degree dispersion, right spread and stop-loss transform orders, etc.
[4] Extremal moment methods : structure of finite atomic random variables, stop-loss ordered extremal
distributions, etc.
[5] Pseudo compound Poisson distributions and their applications
[6] Neyman type confidence intervals : discrete arithmetic case
[7] Fitting parametric models to insurance and financial data
[8] Transform theory : general location and affine transform families, etc.
[9] Coefficient of variation : theory and applications
[10] Maximum likelihood estimation : characterizations, computation, etc.
[11] Parameter orthogonality
[12] Miscellaneous
Actuarial Science and Finance
[1] Aggregate claims models including Bayesian and volatility models
[2] Ordering of risks : Life Table, loss ratios, pricing principles, risk measures, analytical bounds, etc.
[3] Reinsurance : stop-loss contracts, experience rating, solvability, cost of capital, optimisation, etc.
[4] Catastrophic risk : extreme value theory, order statistics, earthquake life reinsurance, etc.
[5] Stochastic tariffing in life insurance
[6] Risk-exchange models
[7] Asset and liability models including immunization theory
[8] Economic risk capital : probability models for insurance and market risk, VaR and CVaR measures,
diversification, risk allocation forms, analytical bounds, optimisation, etc.
[9] Portfolio theory : alternative approaches, portfolio insurance, optioned portfolio selection, CAPM, etc.
[10 ]Option theory : generalized Black-Scholes formulas via stochastic calculus, derivative pricing,
hedging, etc.
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