Emeritus Professor Ross Maller
Areas of expertise
- Stochastic Analysis And Modelling 010406
- Applied Statistics 010401
- Probability Theory 010404
- Statistical Theory 010405
Biography
Maller, Prof. R.A.
E-Professor, School of Finance, Actuarial Studies & Statistics, Australian National University.
Prof. Maller has held a variety of positions relating to Statistics, Probability and Financial Mathematics, ranging from consultant statistician at the CSIRO (1968-1988, including Senior Regional Officer, WA Branch of the Division of Mathematics and Statistics, 1985-1988), to Lecturer and later Professor in the Departments of Mathematics and Statistics and Accounting and Finance at the University of Western Australia. Most recently, he has been Professor of Financial Mathematics, Centre for Mathematical Analysis and School of Finance and Applied Statistics, at the Australian National University, before taking his present position.
He has extensive lecturing experience, having taught Probability and Statistics at all levels from first year through to Honours, and Advanced Finance and Derivatives courses at second, third year and Honours levels. Supervision includes over 24 completed Honours/Diploma students and 9 completed PhD students to date.
Current research interests include Probability, Statistics, Insurance and Quantitative Finance, Quantitative Criminology (Recidivism Studies), Medical Statistics, Survival Analysis.
He has editorial, refereeing, and reviewing experience with major international and Australian mathematical, statistical and applications journals.
Professional visitors and collaborators have included major international figures in Probability/Statistics from the US, UK and Europe. He has been involved in many collaborative research projects in Australia, varying over agriculture, fisheries, medical and especially criminology, applications. He is author of over 150 research papers in probability, statistics and applications journals, and co-author of two books: "Survival Analysis with Long-term Survivors" (with Xian Zhou, Wiley, 1996) and "Mathematical Ecology of Plant Species Competition" (with A.G. Pakes, Camb.Univ. Press, 1989).
He has held a number of ARC and other grants including an ARC Discovery Grant and Australian Professorial Fellowship, 2010-2014.
PRIZES AND HONOURS
G. W. Snedecor Prize, 1984 (American Statistical Association).
RESEARCH INTERESTS
Stochastic Processes, Statistics, Applied Statistics, Probability, Quantitative Finance, Options, Portfolio Analysis, Random Walks, Medical Statistics, Survival Analysis.
Publications
- Maller, R & Shemehsavar, S 2023, 'Generalised Poisson-Dirichlet Distributions Based on the Dickman Subordinator', Theory of Probability and its Applications, vol. 67, no. 4, pp. 593-612.
- Maller, R, Resnick, S, Shemehsavar, S et al. 2022, 'Finite sample and asymptotic distributions of a statistic for sufficient follow-up in cure models [In press]', Canadian Journal of Statistics, vol. online.
- Escobar-Bach, M, Maller, R, Von Keilegom, I, Zhao, Muzhi, 2022, 'Estimation of the cure rate for distributions in the Gumbel maximum domain of attraction under insufficient follow-up', Biometrika, vol. 109, no. 1, pp. 243-256.
- Maller, R & Resnick, S 2021, 'Extremes of censored and uncensored lifetimes in survival data', Extremes, vol. 25, pp. 331-361.
- Buchmann, B, Ferreira, A & Maller, R 2021, 'Convergence of extreme values of Poisson point processes at small times', Extremes, vol. 24, pp. 501-529.
- Fan, Y & Maller, R 2021, 'No-Tie Conditions for Large Values of Extremal Processes', Invited Paper, in Loic Chaumont, Andreas E. Kyprianou (ed.), A Lifetime of Excursions Through Random Walks and Levy Processes: a volume in honour of Ron Doney's 80th birthday,, Progress in Probability, vol 78, Birkhauser Cham., Switzerland, pp. 231-243.
- Fan, Y, Maller, R, Shemehsavar, S 2021, 'A generalised Dickman distribution and the number of species in a negative binomial process model', Advances in Applied Probability, vol. 53, no. 2, pp. 370-399.
- Maller, R & Mason, D 2020, 'Compactness and continuity properties for a Levy process at a two-sided exit time', Electronic Journal of Probability, vol. 25, no. 51, pp. 1-26.
- Huang, F, Maller, R & Ning, X 2020, 'Modelling life tables with advanced ages: An extreme value theory approach', Insurance; Mathematics and Economics, vol. 93, pp. 95-115.
- Jiang, C, Dev, P & Maller, R 2020, 'A Hypothesis Test Method for Detecting Multifractal Scaling, Applied to Bitcoin Prices', Journal of Risk and Financial Management, vol. 13, no. 5, pp. -.
- Ipsen, Y, Maller, R & Resnick, S 2020, 'Trimmed Levy processes and their extremal components', Stochastic Processes and their Applications, vol. 130, no. 4, pp. 2228-2249.
- Ipsen, Y, Maller, R, Shemehsavar, S. 2020, 'Limiting Distributions of Generalised Poisson-Dirichlet Distributions Based on Negative Binomial Processes', Journal of Theoretical Probability, 33, 1974-2000.
- Maller, R & Schindler, T 2019, 'Small time convergence of subordinators with regularly or slowly varying canonical measure', Stochastic Processes and their Applications, vol. 129, no. 10, pp. 4144-4162.
- Ipsen, Y, Maller, R & Resnick, S 2019, 'Ratios of ordered points of point processes with regularly varying intensity measures', Stochastic Processes and their Applications, 129, 205-222.
- Maller, R & Mason, D 2018, 'Matrix normalised stochastic compactness for a Levy process at zero', Electronic Journal of Probability, vol. 23, no. 69, pp. 1-37.
- Buchmann, B, Maller, R & Resnick, S 2018, 'Processes of rth largest, Extremes, 21, 485–508.
- Ipsen, Y, Kevei, P & Maller, R 2018, 'Convergence to Stable Limits for Ratios of Trimmed Levy Processes and their Jumps', Markov Processes and Related Fields, 24, 539-562.
- Maller, R 2018, 'Extensions of Regularity for a Lévy Process', Theory of Probability and its Applications, 62, 575-603.
- Broadhurst, R, Maller, R, Maller, M, Bouhours, B. 2018, 'The Recidivism of Homicide Offenders in Western Australia', Australian & New Zealand Journal of Criminology, 51(3), 395–411. https://doi.org/10.1177/0004865817722393
- Buchmann, B, Ipsen, Y & Maller, R 2017, 'Functional laws for trimmed Levy processes', Advances in Applied Probability 54, 873–889.
- Fan, Y, Griffin, P, Maller, R, Szimayer, A., Wang, T. 2017, 'The Effects of Largest Claim and Excess of Loss Reinsurance on a Company's Ruin Time and Valuation', Risks, 5, no. 3.
- Ipsen, Y.F, & Maller, R 2017, 'Negative Binomial Construction of Random Discrete Distributions on the Infinite Simplex', Theory of Stochastic Processes, 22, 34-46.
- Maller, R and Schmidli, P. 2017, 'Small time almost sure behaviour of extremal processes', Advances in Applied Probability, 49, 411-429.
- 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.
- Maller, R, Roberts, S & Tourky, R 2016, 'The large-sample distribution of the maximum Sharpe ratio with and without short sales', Journal of Econometrics, 194, 138-152.
- Maller, R 2016, 'Small Time Almost Sure Comparisons Between a Levy Process and its Maximal Jump Processes', Markov Processes and Related Fields, 22, 775-806.
- Buchmann, B, Fan, Y. & Maller, R 2016 'Distributional Representations and Dominance of a Levy Process over its Maximal Jump Processes', Bernoulli, 22, 2325-2371.
- Maller, R 2016, 'Conditions for a L\'evy process to stay positive near 0, in probability', Bernoulli, 22, 1963-1978.
- Doney, R., Kluppelberg, C., and Maller, R. 2016, 'Passage Time and Fluctuation Calculations for Subexponential Levy Processes', Bernoulli; 22, 1491-1519.
- Maller, R & Mason, D 2015, 'Matrix normalized convergence of a Levy process to normality at zero', Stochastic Processes and their Applications, 125, 2353-2382.
- 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.
- Maller, R 2015, 'Strong Laws at Zero for Trimmed Levy Processes', Electron. J. Probab. 20, no. 88, 1–24.
- Broadhurst, R & Maller, R 2013, Stopping crime with the power of statistics, 3pp.
- Griffin, P, Maller, R & Roberts, D 2013, 'Finite time ruin probabilities for tempered stable insurance risk processes', Insurance; Mathematics and Economics, vol. 53, no. 2, pp. 478-489.
- Griffin, P. & Maller, R. 2013, 'Small and large time stability of the time taken for a Levy process to cross curved boundaries', Annales de l Institut Henri Poincare B: Probability and Statistics, 49, 208-235.
- Maller, R & Mason, D 2013, 'A characterization of small and large time limit laws for self-normalized Levy process', in "Limit Theorems in Probability, Statistics and Number Theory, Springer Proceedings in Mathematics & Statistics, P. Eichelsbacher et al, Eds., Volume 42, 2013, 141-169. > (ed.), <>, pp. 141-169.
- Griffin, P & Maller, R 2012, 'Path decomposition of ruinous behavior for a general Levy insurance risk process', Annals of Applied Probability, 22, 1411-1449.
- Griffin, P., Maller, R. & van Schaik, K. 2012, 'Asymptotic distributions of the overshoot and undershoots for the Levy insurance risk process in the Cramer and convolution equivalent cases', Insurance; Mathematics and Economics, 51, 382-392.
- Buchmann, B & Maller, R 2011, 'The small-time Chung-Wichura law for Levy processes with non-vanishing Brownian component', Probability Theory and Related Fields, vol. 149, no. 1-2, pp. 303-330.
- Durand, R.B., Gould, J. and Maller, R.A. (2011) On the performance of the minimum VaR portfolio, European Journal of Finance, 17, no. 7, pp. 553-576.
- Bankovsky, D, Kluppelberg, C & Maller, R 2011, 'On the ruin probability of the generalised Ornstein-Uhlenbeck process in the Cramer case', Journal of Applied Probability, vol. 48A, pp. 15-28.
- Behme, A., Lindner, L., Maller, R 2011, 'Stationary solutions of the stochastic differential equation dV_{t} =V_{t} -dU_{t} +dL_{t} with Levy noise', Stochastic Processes and their Applications, vol. 121, no. 1, pp. 91-108.
- Durand, R.B., Maller, R A., Mueller, G. 2011, 'The risk-return tradeoff: A COGARCH analysis of Merton's hypothesis', Journal of Empirical Finance, 18, 306--320.
- Griffin, P.S. and Maller, R 2011, 'Stability of the exit time for Levy processes', Advances in Applied Probability, vol. 43, no. 3, pp. 712-734.
- Griffin, P.S. and Maller, R 2011, 'The time at which a Levy process creeps', Elect. J. Prob., vol. 16, pp. 2182-2202.
- Kluppelberg, C, Maller, R & Szimayer, A 2011, 'The COGARCH: a review, with news on option pricing and statistical inference', in Jochen Blath, Peter Imkeller, Sylvie Reilly (ed.), Surveys in Stochastic Processes, European Mathematical Society Publishing House, Zurich Switzerland, pp. 29-58.
- Maller, R & Mason, D 2010, 'Small-time compactness and convergence behavior of deterministically and self-normalised Levy processes', Transactions of the American Mathematical Society, vol. 362, no. 4, pp. 2205-2248.
- Maller, R, Durand, R & Jafarpour, H 2010, 'Optimal portfolio choice using the maximum Sharpe ratio', The Journal of Risk, vol. 12, no. 4, pp. 49-73.
- Kaehler, B & Maller, R 2010, 'A generalized skewness statistic for stationary ergodic martingale differences', Mathematical Methods of Statistics, vol. 19, no. 3, pp. 267-282.
- Durand, R., Jafarpour, H., Klueppelberg, C., Maller, R 2010, 'Maximize the Sharpe ratio and minimize a VaR', Journal of Wealth Management, vol. 13, no. 1, pp. 91-102.
- Maller, R 2009, 'Small-time versions of Strassen's law for Levy processes', Proceedings of the London Mathematical Society, vol. 98, pp. 531-558.
- Fleischer, P, Maller, R & Muller, G 2009, 'A Bayesian Analysis of Market Information Linkages among NAFTA Countries using a Multivariate Stochastic Volatility Model', Journal of Economics and Finance, vol. Online 28 May 09, p. 26.
- Muller, G, Durand, R, Maller, R, 2009, 'Analysis of Stock Market Volatility by Continuous-time GARCH Models', in Greg N Gregoriou (ed.), Stock Market Volatility, Taylor & Francis Group, Boca Raton, FL, USA, pp. 31-50.
- Maller, R & Mason, D 2009, 'Stochastic Compactness of Levy Processes', in Christian Houdre, Vladimir Koltchinskii, David M. Mason and Magda Peligrad (ed.), High Dimensional Probability V: The Luminy Volume, Institute of Mathematical Statistics, Beachwood, Ohio, USA, pp. 239-257.
- Maller, R, Muller, G & Szimayer, A 2009, 'Ornstein-Uhlenbeck processes and extensions', in Andersen, T.G.; Davis, R.A.; KreiÃ?, J.-P.; Mikosch, Th. (ed.), Handbook of Financial Time Series, Springer, USA, pp. 16 pages.
- Park, H & Maller, R 2008, 'Moment and MGF Convergence of Overshoots and Undershoots for Levy Insurance Risk Processes', Advances in Applied Probability, vol. 40, no. 3, pp. 716 - 733.
- Bertoin, J, Doney, R & Maller, R 2008, 'Passage of Levy processes across power law boundaries at small times', The Annals of Probability, vol. 36, no. 1, pp. 160-197.
- Doney, R, Maller, R & Savov, M 2008, 'Renewal theorems and stability for the reflected process', Stochastic Processes and their Applications, vol. 119, pp. 1270-1297.
- Buchmann, B, Maller, R & Szimayer, A 2008, 'An almost sure functional limit theorem at zero for a class of Levy processes normed by the square root function, and applications', Probability Theory and Related Fields, vol. 142, no. 1-2, pp. 219 - 247.
- Maller, R, Muller, G & Szimayer, A 2008, 'GARCH Modelling in continuous time for irregularly spaced time series data', Bernoulli, vol. 14, no. 2, pp. 519 - 542.
- Bertoin, J, Lindner, A & Maller, R 2008, 'On continuity properties of the law of integrals of Levy processes', in C.Donati-Martin, M.Emery, A.Rouault, C.Stricker (ed.), Seminaire de Probabilites XLI, Springer, Berlin, pp. 137-159.
- Brokate, M, Kluppelberg, C, Kostadinova, R , Maller, R. 2008, 'On the distribution tail of an integrated risk model: A numerical approach', Insurance; Mathematics and Economics, vol. 42, pp. 101-106.
- Maller, R & Mason, D 2008, 'Convergence in distribution of Levy processes at small times with self-normalization', Acta Scientiarum Mathematicarum, vol. 74, pp. 315 - 347.
- Erickson, K & Maller, R 2007, 'Finiteness of Integrals of Functions of Levy Processes', Proceedings of the London Mathematical Society, vol. 94, no. 3, pp. 386-420.
- Doney, R & Maller, R 2007, 'Almost sure relative stability of the overshoot of power law boundaries', Journal of Theoretical Probability, vol. 20, no. 1, pp. 47-63.
- Szimayer, A & Maller, R 2007, 'Finite approximation schemes for Levy processes, and their application to optimal stopping problems', Stochastic Processes and their Applications, vol. 117, pp. 1422-1447.
- Doney, R & Maller, R 2007, 'Curve crossing for random walks reflected at their maximum', Annals of Applied Probability, vol. 35, no. 4, pp. 1351-1373.
- Maller, R, Solomon, D & Szimayer, A 2006, 'A Multinomial Approximation for American Option Prices in Levy Process Models', Mathematical Finance, vol. 16, no. 4, pp. 613-633.
- Kluppelberg, C, Lindner, A & Maller, R 2006, 'Continuous time volatility modelling: COGARCH versus Ornstein-Uhlenbeck models', in Yuri Kabanov, Robert Lipster (ed.), From stochastic calculus to mathematical finance, Springer, Germany, pp. 393-419.
- Erickson, K & Maller, R 2005, 'Drift to Infinity and the Strong Law for Subordinated Random Walks and Levy Processes', Journal of Theoretical Probability, vol. 18, no. 2, pp. 359-375.
- Doney, R & Maller, R 2005, 'Cramers estimate for a reflected Levy process', The Annals of Probability, vol. 15, pp. 1-6.
- Doney, R & Maller, R 2005, 'Passage times of random walks and Levy processes across power law boundaries', Probability Theory and Related Fields, vol. 133, no. 1, pp. 57-70.
- Maller, R, Durand, R & Lee, P 2005, 'Bias and consistency of the maximum Sharpe ratio', The Journal of Risk, vol. 7, no. 4, pp. 103-115.
- Erickson, K & Maller, R 2005, 'Generalised Ornstein-Uhlenbeck processes and the convergence of Levy integrals', in J-M Morel, F Takens, B Teissier (ed.), Seminaire de Probabilites XXXVIII, Springer, Germany, pp. 70-94.
- Lindner, A & Maller, R 2005, 'Levy integrals and the Stationarity of generalised Ornstein-Uhlenbeck processes', Stochastic Processes and their Applications, vol. 115, no. 10, pp. 1701-1722.
- Kluppelberg, C, Lindner, A & Maller, R 2004, 'A continous-time GARCH process driven by a Levy process: stationarity and second-order behaviour', Journal of Applied Probability, vol. 41, pp. 601-622.
- Szimayer, A & Maller, R 2004, 'Testing for mean reversion in processes of Ornstein-Uhlenbeck type', Statistical Inference for Stochastic Processes, vol. 7, pp. 95-113.
- Doney, R & Maller, R 2004, 'Moments of passage times for Levy processes', Annales de l Institut Henri Poincare B: Probability and Statistics, vol. 40, pp. 279-297.
- Durack, N, Durand, R & Maller, R 2004, 'A best choice among asset pricing models? The conditional capital asset pricing model in Australia', Accounting and Finance, vol. 44, pp. 139-162.
- Kesten, H & Maller, R 2004, 'Some effects of trimming on the law of the iterated logarithm', Journal of Applied Probability, vol. 41A, pp. 253-271.
- Kluppelberg, C., Kyprianou, A. & Maller, R. 2004, 'Ruin probabilities and overshoots for general Levy insurance risk processes', Annals of Applied Probability, 14, 1766-1801.
- Maller, R 2003, 'Asymptotics of regressions with stationary and nonstationary residuals', Stochastic Processes and their Applications, vol. 105, pp. 33-67.
- Maller, R & Zhou, X 2003, 'Testing for Individual Heterogeneity in Parametric Models for Event-History Data', Mathematical Methods of Statistics, vol. 12, no. 3, pp. 276-304.