Michael Kalkbrener


Mathematical Finance

Computer Algebra

Solving systems of algebraic equations by using Gröbner bases. Proc. EUROCAL’87, Springer LNCS 378, 282-291, Leipzig, Germany, 1987. [Kalkbrener87.pdf]

Implicitization of rational parametric curves and surfaces. Proc. AAECC-8, Springer LNCS 508, 249-259, Tokyo, Japan, 1990. [Kalkbrener90.pdf]

A generalized Euclidean algorithm for computing triangular representations of algebraic varieties. Journal of Symbolic Computation 15, 143-167, 1993. [Kalkbrener93.pdf]

Low degree solutions to linear equations with K[x] coefficients. Journal of Symbolic Computation 16, 75-81, 1993. (Coauthors: M. Sweedler, L. Taylor). [KalkbrenerSweedlerTaylor93.pdf]

Prime decompositions of radicals in polynomial rings. Journal of Symbolic Computation 18, 365-372, 1994. [Kalkbrener94.pdf]

Primitive polynomial remainder sequences in elimination theory. Applicable Algebra in Engineering, Communication and Computing 6, 65-79, 1995.

A generalized Euclidean algorithm for geometry theorem proving. Annals of Mathematics and Artificial Intelligence 13, 73-95, 1995. [Kalkbrener95.pdf]

Initial complexes of prime ideals. Advances in Mathematics 116, 365-376, 1995. (Coauthor: B. Sturmfels). [KalkbrenerSturmfels95.pdf]

On the stability of Gröbner bases under specializations. Journal of Symbolic Computation 24, 51-58, 1997. [Kalkbrener97a.pdf]

Converting bases with the Gröbner walk. Journal of Symbolic Computation 24, 465-469, 1997. (Coauthors: S. Collart, D. Mall). [CollartKalkbrenerMall97.pdf]

An upper bound on the number of monomials in determinants of sparse matrices with symbolic entries. Mathematica Pannonica 8, 73-82, 1997. [Kalkbrener97b.pdf]

Algorithmic properties of polynomial rings. Journal of Symbolic Computation 26, 525-581, 1998. [Kalkbrener98.pdf]

On the complexity of Gröbner bases conversion. Journal of Symbolic Computation 28, 265-273, 1999. [Kalkbrener99.pdf]

The maturity effect on credit risk capital. RISK (July 2002), 59-63. (Coauthor: L. Overbeck). [KalkbrenerOverbeck02.pdf]

Risk management of non-maturing liabilities. Journal of Banking and Finance 28(7), 1547-1568, 2004. (Coauthor: J. Willing). [KalkbrenerWilling04.pdf]

Sensible and efficient capital allocation for credit portfolios. RISK (Jan. 2004), S19-S24. (Coauthors: H. Lotter, L. Overbeck). [KalkbrenerLotterOverbeck04.pdf]

A fundamental look at economic capital and risk-based profitability measures. In Dev, A (ed.): Economic Capital: A Practitioner Guide, 211-230, Risk Books, 2004. (Coauthors: S. Fritz, W. Paus). [FritzKalkbrenerPaus04.pdf]

An axiomatic approach to capital allocation. Mathematical Finance 15(3), 425-437, 2005. [Kalkbrener05.pdf]

LDA at work: Deutsche Bank’s approach to quantifying operational risk. Journal of Operational Risk 1(4), 49-93, 2006. (Coauthor: F. Aue). [AueKalkbrener06.pdf]

Credit risk concentrations under stress. Journal of Credit Risk 2(3), 115-136, 2006. (Coauthors: G. Bonti, C. Lotz, G. Stahl). [BontiKalkbrenerLotzStahl06.pdf]

Efficient calculation of expected shortfall contributions in large credit portfolios. Journal of Computational Finance 11, 45-77, 2007. (Coauthors: A. Kennedy, M. Popp). [KalkbrenerKennedyPopp07.pdf]

Mathematics in financial risk management. Jahresbericht der Deutschen Mathematiker Vereinigung 109(4), 165-194, 2007. (Coauthors: E. Eberlein, R. Frey, L. Overbeck). [EberleinFreyKalkbrenerOverbeck07.pdf]

An axiomatic characterization of capital allocations of coherent risk measures. Quantitative Finance 9(8), 961-965, 2009. [Kalkbrener09.pdf]

Validating structural credit portfolio models. In Rösch, D., Scheule, H. (eds): Model Risk - Challenges and Solution for Financial Risk Models, 233-262, Risk Books, 2010. (Coauthor: A. Onwunta). [KalkbrenerOnwunta10.pdf]

On the aggregation of risk. Journal of Risk 12(3), 45-68, 2010. (Coauthor: M. Brockmann). [BrockmannKalkbrener10.pdf]

Correlations under stress in normal variance mixture models. Mathematical Finance, 25:2, 426-456, 2015. (Coauthor: N. Packham). [KalkbrenerPackham2012.pdf]

Stress testing of credit portfolios in light- and heavy-tailed models. Journal of Risk Management in Financial Institutions, 8:1, 34-44, 2015. (Coauthor: N. Packham).[KalkbrenerPackham2014.pdf]

Asymptotic behaviour of multivariate default probabilities and default correlations under stress. Journal of Applied Probability, 53:1, 2016. (Coauthors: N. Packham, L. Overbeck). [PackhamKalkbrenerOverbeck2015.pdf]

Stress testing in credit portfolio models. In Härdle, W.K., Chen C.Y.H., Overbeck, L. (eds): Applied Quantitative Finance, 153-176, Springer, 2017. (Coauthor: L. Overbeck).



Operational risk measurement beyond the loss distribution approach: an exposure-based methodology. Journal of Operational Risk 13 (2), 1-33, 2018. (Coauthors: M. Einemann, J. Fritscher).