331:
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", which offered a broader modelling framework with new relevant phenomena, 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.
31:
330:
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, while critiquing the existing classical mathematical finance theory.
321:
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
247:
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 and has been a Director of the Scientific Association of Mathematical Finance since 2021.
322:
with Wagner, he discovered the stochastic Taylor formula, and then developed systematically a theory for the efficient numerical solution of stochastic differential equations. With various co-authors, he made seminal contributions on numerical stability, and stochastic delay equations.
297:
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."
240:, 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
309:, 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." He also co-wrote the book
244:. 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.
284:
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
653:
1171:
931:
410:
KΓΌchler, U. & Platen, E. (2000). Strong discrete time approximation of stochastic differential equations with time delay. Mathematics and
Computers in Simulation, 54, 189β205.
401:
Milstein, G.N., Platen, E. & Schurz, H. (1998). Balanced implicit methods for stiff stochastic systems. SIAM Journal on
Numerical Analysis, 35 (3), 1010β1019.
36:
431:
Fergusson, K. & Platen, E. (2023). Less-expensive long-term annuities linked to mortality, cash and equity. Annals of
Actuarial Science. 17, 170β207.
398:
Hofmann, N., Platen, E. & Schweizer, M. (1992). Option pricing under incompleteness and stochastic volatility. Mathematical
Finance, 2 (3), 153β187.
416:
Craddock, M. & Platen, E. (2004). Symmetry group methods for fundamental solutions. Journal of
Differential Equations, 207 (2), 285β302.
213:
107:
428:
Baldeaux, J. & Ignatieva, K. & Platen, E. (2017). Detecting money market bubbles. Journal of
Banking & Finance. 87, 369β379.
395:
Platen, E. & Wagner W. (1982) On a Taylor formula for a class of Ito processes. Probability and
Mathematical Statistics, 3 (1), 37β51.
1146:
422:
Filipovic, D. & Platen, E. (2009). Consistent market extensions under the benchmark approach. Mathematical Finance, 19 (1), 41β52.
503:
153:
241:
189:
146:
122:
1161:
1141:
233:
185:
1151:
407:
Platen, E. (1999). An introduction to numerical methods for stochastic differential equations. Acta Numerica, 8, 197β246.
404:
Platen, E. & Schweizer, M. (1998). On feedback effects from hedging derivatives. Mathematical Finance, 8 (1), 67β84.
556:"Numerical Solutions of Stochastic Differential Equations (Kloeden, P.K. And Platen, E.; 2008) [Book reviews]"
232:
from 1987 to 1990. Later, in 1991, he assumed the role of Senior Fellow at the Institute of Advanced Studies at the
1166:
1156:
485:
413:
Platen, E. (2002). Arbitrage in continuous complete markets. Advances in Applied Probability, 33 (2), 540β558.
313:
with Jan Baldeaux, which explored the systemic derivation of explicit formulas for functionals of diffusions.
522:
425:
Du, K. & Platen, E. (2016). Benchmarked risk minimization. Mathematical Finance. doi: 10.1111/mafi.12065
181:
164:
theory by his benchmark approach. He has authored and co-authored research papers and five books including
1181:
691:
Milstein, G. N.; Platen, E.; Schurz, H. (1998). "Balanced Implicit Methods for Stiff Stochastic Systems".
761:
225:
993:
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60:
30:
586:
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205:
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by studying numerical methods and quantitative finance and proposing the benchmark approach for
1121:
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617:"Functionals of multidimensional diffusions with applications to finance | WorldCat.org"
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673:
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567:
471:
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Platen, E. (2006). A benchmark approach to finance. Mathematical Finance, 16 (1), 131β151.
1024:
728:"Strong discrete time approximation of stochastic differential equations with time delay"
1081:
669:
777:
743:
1135:
1009:
978:
138:
56:
811:
145:, academic, and author. He is an emeritus Professor of Quantitative Finance at the
1114:"Entropy-Maximizing Dynamics of Continuous Markets by Eckhard Platen :: SSRN"
602:
587:"A Benchmark Approach to Quantitative Finance, by Eckhard Platen and David Heath"
257:
201:
81:
555:
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875:
843:
826:
704:
677:
616:
229:
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at the Academy of Sciences Berlin, holding the position of Head of the Sector
209:
103:
98:
947:
571:
454:
371:
Numerical Solution of Stochastic Differential Equations with Jumps in Finance
295:
Numerical Solution of Stochastic Differential Equations with Jumps in Finance
916:
859:
654:"An introduction to numerical methods for stochastic differential equations"
273:
269:
827:"Less-expensive long-term annuities linked to mortality, cash and equity"
237:
383:
Functionals of Multi-dimensional Diffusions with Applications to Finance
311:
Functionals of Multi-dimensional Diffusions with Applications to Finance
174:
Functionals of Multi-dimensional Diffusions with Applications to Finance
1049:
1040:
712:
536:
265:
157:
91:
1098:
884:
760:
Hofmann, Norbert; Platen, Eckhard; Schweizer, Martin (July 12, 1992).
794:
Baldeaux, Jan; Ignatieva, Katja; Platen, Eckhard (February 1, 2018).
301:
Later, Platen published monographs on his benchmark approach, namely
224:
Platen began his academic career in 1975 as a Research Fellow at the
762:"Option Pricing Under Incompleteness and Stochastic Volatility"
152:
Platen is most known for his research on numerical methods for
504:"Quant Guide 2020: University of Technology Sydney - Risk.net"
994:"Consistent Market Extensions Under the Benchmark Approach"
343:
2015 β Honorary Professor, Australian National University
899:
Platen, Eckhard; Schweizer, Martin (January 12, 1998).
359:
Numerical Solution of Stochastic Differential Equations
317:
Numerical solution of stochastic differential equations
287:
Numerical Solution of Stochastic Differential Equations
166:
Numerical Solution of Stochastic Differential Equations
992:
FilipoviΔ, Damir; Platen, Eckhard (January 12, 2009).
365:
Numerical Solution of SDE Through Computer Experiments
291:
Numerical Solution of SDE Through Computer Experiments
176:. He is the recipient of the 1992 Best Paper Award in
1172:
Academic staff of the University of Technology Sydney
1064:
Craddock, Mark; Platen, Eckhard (December 15, 2004).
825:
Fergusson, Kevin; Platen, Eckhard (March 12, 2023).
16:
German/Australian mathematician, financial economist
726:KΓΌchler, Uwe; Platen, Eckhard (November 30, 2000).
118:
113:
97:
76:
71:
52:
44:
21:
1066:"Symmetry group methods for fundamental solutions"
340:2014 β Honorary Professor, University of Cape Town
860:"A Fair Pricing Approach to Weather Derivatives"
486:"Fellows of the Australian Mathematical Society"
160:along with the generalization of the classical
901:"On Feedback Effects from Hedging Derivatives"
858:Platen, Eckhard; West, Jason (March 1, 2004).
8:
377:A Benchmark Approach to Quantitative Finance
303:A Benchmark Approach to Quantitative Finance
170:A Benchmark Approach to Quantitative Finance
523:"Former members of the Executive Committee"
932:"Arbitrage in continuous complete markets"
585:Runggaldier, Wolfgang (October 12, 2011).
188:from 2015 to 2020, and is a Fellow of the
29:
18:
1097:
1048:
1023:Du, Ke; Platen, Eckhard (July 12, 2016).
883:
842:
732:Mathematics and Computers in Simulation
441:
256:Platen has contributed to the field of
930:Platen, Eckhard (September 12, 2002).
789:
787:
755:
753:
212:, followed by a DSc in Science at the
180:, was named Honorary Professor at the
466:
464:
449:
447:
445:
7:
961:Platen, Eckhard (January 12, 2006).
652:Platen, Eckhard (January 12, 1999).
560:IEEE Transactions on Neural Networks
293:with Kloeden and Henri Schurz, and
778:10.1111/j.1467-9965.1992.tb00027.x
693:SIAM Journal on Numerical Analysis
305:with David Heath. In a review for
14:
1070:Journal of Differential Equations
963:"A Benchmark Approach to Finance"
154:stochastic differential equations
1010:10.1111/j.1467-9965.2008.00356.x
979:10.1111/j.1467-9965.2006.00265.x
800:Journal of Banking & Finance
796:"Detecting money market bubbles"
1025:"Benchmarked Risk Minimization"
936:Advances in Applied Probability
490:Australian Mathematical Society
242:University of Technology Sydney
190:Australian Mathematical Society
147:University of Technology Sydney
123:University of Technology Sydney
864:Asia-Pacific Financial Markets
812:10.1016/j.jbankfin.2017.10.017
234:Australian National University
186:Australian National University
1:
744:10.1016/S0378-4754(00)00224-X
184:from 2014 to 2019 and at the
603:10.1080/14697688.2011.620979
210:Technical University Dresden
104:Technical University Dresden
831:Annals of Actuarial Science
214:Academy of Sciences, Berlin
1198:
385:(2013) ISBN 978-3319007465
379:(2006) ISBN 978-3540262121
373:(2010) ISBN 978-3642120572
367:(1994) ISBN 978-3540570745
361:(1992) ISBN 978-3540540625
108:Academy of Sciences Berlin
1147:Australian mathematicians
1090:10.1016/j.jde.2004.07.026
876:10.1007/s10690-005-4252-9
844:10.1017/S1748499522000112
705:10.1137/S0036142994273525
678:10.1017/S0962492900002920
156:and their application in
128:
67:
28:
572:10.1109/tnn.2008.2008405
200:Platen earned an MSc in
917:10.1111/1467-9965.00045
554:Gianfelici, F. (2008).
182:University of Cape Town
137:is a German/Australian
948:10.1239/aap/1033662165
1162:Australian economists
1142:German mathematicians
226:Weierstrass Institute
204:in 1972 and a PhD in
63:, academic and author
1152:Financial economists
1116:. 24 December 2023.
1029:Mathematical Finance
998:Mathematical Finance
967:Mathematical Finance
905:Mathematical Finance
766:Mathematical Finance
591:Quantitative Finance
307:Quantitative Finance
289:with Peter Kloeden,
178:Mathematical Finance
162:mathematical finance
1082:2004JDE...207..285C
670:1999AcNum...8..197P
621:search.worldcat.org
521:Office, Bachelier.
510:. February 5, 2020.
262:financial economics
143:financial economist
72:Academic background
61:financial economist
1041:10.1111/mafi.12065
639:mathscinet.ams.org
326:Benchmark approach
206:Probability Theory
87:Probability Theory
1167:TU Dresden alumni
1157:German economists
597:(10): 1457β1458.
390:Selected articles
335:Awards and honors
208:in 1975 from the
132:
131:
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822:
816:
815:
791:
782:
781:
757:
748:
747:
723:
717:
716:
699:(3): 1010β1019.
688:
682:
681:
649:
643:
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631:
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624:
613:
607:
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472:"Eckhard Platen"
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1128:
1127:
1105:
1076:(2): 285β302.
1056:
1035:(3): 617β637.
1015:
984:
973:(1): 131β151.
953:
942:(3): 540β558.
922:
891:
850:
837:(1): 170β207.
817:
783:
772:(3): 153β187.
749:
738:(1): 189β205.
718:
683:
644:
626:
608:
577:
546:
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23:Eckhard Platen
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53:Occupation(s)
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43:
38:
32:
27:
20:
1108:
1073:
1069:
1059:
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1028:
1018:
1004:(1): 41β52.
1001:
997:
987:
970:
966:
956:
939:
935:
925:
911:(1): 67β84.
908:
904:
894:
870:(1): 23β53.
867:
863:
853:
834:
830:
820:
803:
799:
769:
765:
735:
731:
721:
696:
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638:
635:"MathSciNet"
629:
620:
611:
594:
590:
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566:(11): 1991.
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559:
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540:
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508:www.risk.net
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119:Institutions
1177:1949 births
1050:10453/36413
806:: 369β379.
664:: 197β246.
537:"Directors"
258:mathematics
230:Stochastics
202:Mathematics
82:Mathematics
37:Oberwolfach
1136:Categories
1099:10453/3413
885:10453/5261
436:References
99:Alma mater
35:Platen at
274:economics
270:insurance
216:in 1985.
196:Education
77:Education
252:Research
238:Canberra
1122:4675048
1078:Bibcode
713:2587119
666:Bibcode
266:finance
158:finance
92:Science
39:in 2023
1120:
711:
220:Career
85:PhD.,
80:MSc.,
709:JSTOR
353:Books
280:Works
90:DSc,
1118:SSRN
541:SAMF
272:and
260:and
172:and
48:1949
45:Born
1094:hdl
1086:doi
1074:207
1045:hdl
1037:doi
1006:doi
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880:hdl
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
