Dr Boris Buchmann



Research School of Finance, Actuarial Studies & Statistics

Associate Professor
Phone number
+61 2 612 57296
Room 4.03, CBE Bld (26C)
Research areas

Statistics; Stochastic analysis and modelling.


Boris Buchmann is an Associate Professor of Statistics.  He is a mathematician working in the general areas of probability theory, mathematical statistics and mathematical finance. 

Boris’ research, collaboration, and supervision focus on infinitely divisible distributions and Lévy processes. His ongoing research projects also include extremal processes and local behaviour of Lévy processes.  Previously, Boris worked on stochastic differential equations driven by fractional Brownian motion, and discovered a statistical convolution logarithm, i.e. decompounding. Boris discovered the notion of weak subordination, to improve on modelling dependence deficiency in an existing finance model but contribute to the notion of time change in high dimensions. He also discovered Le Cam deficiency limits of GARCH, and he derived limiting laws in terms of fractional Brownian motion of OLS estimators in nearly nonstationary models driven by long-range dependent noise. Boris’s research has featured in leading journals including Annals of Statistics, Probability Theory and Related FieldsTransactions of the American Mathematical SocietyBernoulli: A Journal of Mathematical Statistics and ProbabilityAnnals of the Institute of Statistical MathematicsStochastic Processes and their Applications and Advances in Applied Probability. Boris is recipient of Australian Research Council Discovery Program funding, having been awarded a Discovery Project Grant for the project entited Frontiers of Risk Modelling: Dependence and Extremes of Levy Processes.

View ORCID profile

Research publications

Buchmann, B, Lu, K & Madan, D 2019, 'Weak subordination of multivariate Lévy processes and variance generalised gamma convolutions', Bernoulli, 25, pp. 742-770.

Buchmann, B, Lu, K & Madan, D 2020, 'Self-Decomposability of weak variance generalised gamma convolutions', Stochastic Processes and their Applications 1, pp. 630-655.

Buchmann, B, Lu, K & Madan, D 2019, 'Calibration for Weak Variance-Alpha-Gamma Processes', Methodology and Computing in Applied Probability, 21, 1151--1164

Buchmann, B, Maller, R & Resnick, S 2018, 'Processes of rth largest, Extremes, 21, 485–508.

Buchmann, B, Ipsen, Y & Maller, R 2017, 'Functional laws for trimmed Levy processes', Advances in Applied Probability 54, 873–889.

Buchmann, B, Kaehler, B, Maller, R, Szimayer, A. 2017, 'Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing', Stochastic Processes and their Applications 127, 2208--2242.

Buchmann, B, Fan, Y. & Maller, R 2016 'Distributional Representations and Dominance of a Levy Process over its Maximal Jump Processes', Bernoulli, 22, 2325-2371.

Buchmann, B, Maller, R & Mason, D 2015, 'Laws of the iterated logarithm for self-normalised Levy processes at zero', Transactions of the American Mathematical Society, 367, 1737-1770.

Buchmann, B & Chan, N 2013, 'Unified asymptotic theory for nearly unstable AR(p) processes', Stochastic Processes and their Applications, vol. 123, no. 3, pp. 952-985.

Buchmann, B & Müller, G 2012, 'Limit experiments of GARCH', Bernoulli, vol. 18, no. 1, pp. 64-99.

Buchmann, B & Maller, R A 2011, 'The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component.' Probability Theory and Related Fields, vol. 149, no. 1-2, pp. 303--330.

Buchmann, B & Chan, N H 2009, 'Integrated functionals of normal and fractional processes.' Annals of Applied Probability, vol. 19, no. 1, 49--70.

Buchmann, B. 2009, 'Weighted empirical processes in the nonparametric inference for Lévy processes.' Mathematical Methods of Statistics, vol. 18, no. 4, pp. 281--309.

Buchmann, B, Maller, R A & Szimayer, A 2008, 'An almost sure functional limit theorem at zero for a class of Lévy processes normed by the square root function, and applications.' Probability Theory and Related Fields, vol. 142, no. 1-2, pp. 219-247.

Buchmann, B & Weber, S 2007, 'A continuous time approximation of an evolutionary stock market.', International Journal of Theoretical and Applied Finance, vol. 10, no. 7, pp. 1229--1253.

Buchmann, B & Chan, N H 2007, 'Asymptotic theory of least squares estimators for nearly unstable processes under strong dependence', Annals of Statistics, vol. 35, no. 5, pp. 2001-2017.

Buchmann, B & Klüppelberg, C 2006, 'Fractional Integral Equations and State Space Transforms', Bernoulli, vol. 12, no. 3, pp. 431-456.

Buchmann, B & Klüppelberg, C 2005, 'Maxima of stochastic processes driven by fractional Brownian motion', Advances in Applied Probability, vol. 37, no. 3, pp. 743-764.

Buchmann, B & Klüppelberg, C 2004, 'Extremal Behaviour of Fractal Models', Statistics in Finance, ed. Richard Davis and Claudia Kluppelberg, Mathematisches Forschungsinstitut Oberwolfach, Germany, pp. 121-123.

Buchmann, B & Grübel, R 2004, 'Decompounding Poisson random sums: recursively truncated estimates in the discrete case.' Annals of the Institute of Statistical Mathematics, vol. 56, no. 4, pp. 743-756.

Buchmann, B & Grübel, R 2003, 'Decompounding: an estimation problem for Poisson random sums', Annals of Statistics, vol. 31, no. 4, pp. 1054-1074.

Research grants and awards

ARC Discovery Project, DP160104737, Frontiers of Risk Modelling: Dependence and Extremes of Levy Processes, 2016.

Research engagement and outreach

ARC Discovery Project, DP160104737, Frontiers of Risk Modelling: Dependence and Extremes of Levy Processes, 2016.


MATH3029 Probability Modelling with Applications

STAT3004 Stochastic Modelling