Eckhard Platen is a German/Australian mathematician, financial economist, academic, and author. He is an emeritus Professor of Quantitative Finance at the University of Technology Sydney. ^[1]

Platen is most known for his research on numerical methods for stochastic differential equations and their application in finance along with the generalization of the classical mathematical finance theory by his benchmark approach. ^[2] He has authored and co-authored research papers and five books including Numerical Solution of Stochastic Differential Equations, A Benchmark Approach to Quantitative Finance and Functionals of Multi-dimensional Diffusions with Applications to Finance. He is the recipient of the 1992 Best Paper Award in Mathematical Finance, was named Honorary Professor at the University of Cape Town from 2014 to 2019 and at the Australian National University from 2015 to 2020, and is a Fellow of the Australian Mathematical Society. ^[3]

Education

Platen earned an MSc in Mathematics in 1972 and a PhD in Probability Theory in 1975 from the Technical University Dresden, followed by a DSc in Science at the Academy of Sciences, Berlin in 1985. ^[1]

Career

Platen began his academic career in 1975 as a Research Fellow at the Weierstrass Institute at the Academy of Sciences Berlin, holding the position of Head of the Sector Stochastics from 1987 to 1990. Later, in 1991, he assumed the role of Senior Fellow at the Institute of Advanced Studies at the Australian National University in Canberra, serving as the Founding Head of the Centre for Financial Mathematics from 1994 to 1997. In 1997, he took on a joint appointment between the School of Finance and Economics and the School of Mathematical Sciences, and as the chair in Quantitative Finance at the University of Technology Sydney. ^[4] He remained a Research Director of the Quantitative Finance Research Centre at the University of Technology Sydney from 1998 until 2021 and has held the position of emeritus Professor of Quantitative Finance since 2021. ^[1]

Platen founded the Quantitative Methods in Finance annual conference series in 1993, where he served as chair for 25 years. Later, he became President of the Bachelier Finance Society from 2014 to 2015 ^[5] and has been a Director of the Scientific Association of Mathematical Finance since 2021. ^[6]

Research

Platen has contributed to the field of mathematics and financial economics by studying numerical methods and quantitative finance and proposing the benchmark approach for finance, insurance and economics. ^[2]

Works

Platen has authored and co-authored five books on numerical methods and quantitative finance. Earlier, he focused on the numerical solution of stochastic differential equations, writing three books on the topic including Numerical Solution of Stochastic Differential Equations with Peter Kloeden, Numerical Solution of SDE Through Computer Experiments with Kloeden and Henri Schurz, and Numerical Solution of Stochastic Differential Equations with Jumps in Finance with Nicola Bruti-Liberati. About the first book, Francesco Gianfelici remarked, "...the need for proper SDE methodologies in a numerical context is increasingly pressing and provides the motivation and the starting point of this excellent book written by Kloeden and Platen." ^[7]

Later, Platen published monographs on his benchmark approach, namely A Benchmark Approach to Quantitative Finance with David Heath. In a review for Quantitative Finance, Wolfgang Runggaldier commented "The book thus presents itself as a comprehensive treatment of Quantitative Finance and distinguishes itself from analogous treatments by using a novel approach, namely the benchmark approach." ^[8] He also co-wrote the book Functionals of Multi-dimensional Diffusions with Applications to Finance with Jan Baldeaux, which explored the systemic derivation of explicit formulas for functionals of diffusions. ^[9]

Numerical solution of stochastic differential equations

Platen's work on stochastic differential equations has focused on a general theory for their numerical solution. He contended that the availability of a stochastic analogue to the deterministic Taylor formula would be essential for a numerical theory for stochastic differential equations. Together with Wagner, he discovered the stochastic Taylor formula, ^[10] and then developed systematically a theory for the efficient numerical solution of stochastic differential equations. ^[11] With various co-authors, he made seminal contributions on numerical stability, ^[12] and stochastic delay equations. ^{[13] [14] [15] [16] [17]}

Benchmark approach

Platen studied finance theory and proposed the benchmark approach as a novel, very general modelling method. Since the 1990s, he has focused on financial market modelling, derivative pricing, insurance and long-term risk management, ^{[14] [18]} while critiquing the existing classical mathematical finance theory. ^[19] He concluded that the best performing portfolio of a market, which can be found by maximizing its expected growth rate, should form the centrepiece of a more general finance theory that he called the "benchmark approach", ^[20] which offered a broader modelling framework with new relevant phenomena, ^{[21] [22] [15]} and he presented its systematic formulation first in his books and later in research. Using Li symmetry group methods and entropy maximization, he identified conservation laws in finance, in the sense of Noether's Theorem, and discovered the typical least disturbed financial market dynamics. ^{[23] [24]}

Awards and honors

• 2014 – Honorary Professor, University of Cape Town
• 2015 – Honorary Professor, Australian National University

Bibliography

Books

• Numerical Solution of Stochastic Differential Equations (1992) ISBN 978-3540540625
• Numerical Solution of SDE Through Computer Experiments (1994) ISBN 978-3540570745
• Numerical Solution of Stochastic Differential Equations with Jumps in Finance (2010) ISBN 978-3642120572
• A Benchmark Approach to Quantitative Finance (2006) ISBN 978-3540262121
• Functionals of Multi-dimensional Diffusions with Applications to Finance (2013) ISBN 978-3319007465

Selected articles

• Platen, E. & Wagner W. (1982) On a Taylor formula for a class of Ito processes. Probability and Mathematical Statistics, 3 (1), 37–51.
• Hofmann, N., Platen, E. & Schweizer, M. (1992). Option pricing under incompleteness and stochastic volatility. Mathematical Finance, 2 (3), 153–187.
• Milstein, G.N., Platen, E. & Schurz, H. (1998). Balanced implicit methods for stiff stochastic systems. SIAM Journal on Numerical Analysis, 35 (3), 1010–1019.
• Platen, E. & Schweizer, M. (1998). On feedback effects from hedging derivatives. Mathematical Finance, 8 (1), 67–84.
• Platen, E. (1999). An introduction to numerical methods for stochastic differential equations. Acta Numerica, 8, 197–246.
• Küchler, U. & Platen, E. (2000). Strong discrete time approximation of stochastic differential equations with time delay. Mathematics and Computers in Simulation, 54, 189–205.
• Platen, E. (2002). Arbitrage in continuous complete markets. Advances in Applied Probability, 33 (2), 540–558.
• Craddock, M. & Platen, E. (2004). Symmetry group methods for fundamental solutions. Journal of Differential Equations, 207 (2), 285–302.
• Platen, E. (2006). A benchmark approach to finance. Mathematical Finance, 16 (1), 131–151.
• Filipovic, D. & Platen, E. (2009). Consistent market extensions under the benchmark approach. Mathematical Finance, 19 (1), 41–52.
• Du, K. & Platen, E. (2016). Benchmarked risk minimization. Mathematical Finance. doi: 10.1111/mafi.12065
• Baldeaux, J. & Ignatieva, K. & Platen, E. (2017). Detecting money market bubbles. Journal of Banking & Finance. 87, 369–379.
• Fergusson, K. & Platen, E. (2023). Less-expensive long-term annuities linked to mortality, cash and equity. Annals of Actuarial Science. 17, 170–207.

References