Official Title: Assistant Professor

Faculty: Faculty of Business and Law


Short Bio

Ivan Arraut is a PhD graduated from the school of Science at Osaka University. His research areas include Game Theory for applications in Business and Economy, Quantum Finance, Business Analytics and Machine Learning as well as fundamental researches in Physics and Engineering sciences. Ivan Arraut thinks that Science and Business cannot be separated because both areas need from each other in order to progress and he has learned how to combine successfully both of them. In fact, some of Ivan's best results came out by mapping some ideas from Business and economy toward fundamental sciences and viceversa, namely, by mapping ideas from fundamental sciences into ideas related to Business, economy and Financial areas. Ivan Arraut is then a multidisciplinary researcher, teaching quantitative courses at USJ in Macau. Ivan is also interested in entrepreneurship, mainly on the industries touching data analysis, financial technology, machine learning, video games, development of apps and visual animation.
Ivan Arraut has a long history in research and more than 5 years of teaching experience in different universities. He has received 10 academic prizes and/or recognitions from different institutions around the world during his career.



1). Ivan Arraut, Alan Au, Alan Tse and Carlos Segovia, “The connection between multiple prices of an Option at a given time with single prices defined at different times: The concept of weak-value in quantum finance”, Physica A, Vol. 526, 121028, (2019).

2). Ivan Arraut, Alan Au and Alan Tse, “Spontaneous symmetry breaking in Quantum Finance”, EPL 131 (2020) 6, 68003.

3). Ivan Arraut, “Black-Hole evaporation from the perspective of neural networks”, 2018 EPL 124 50002.

4). Ivan Arraut and Diana Diaz, “On the loss of learning capability inside an arrangement of neural networks: The bottleneck effect in Black-Holes”, Symmetry 2020, 12, 1484.

5). Ivan Arraut, Alexandre Lobo and Sergio Gomes, “The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance”, Mathematics 2021, 9(21), 2777.

6). Ivan Arraut, Alexandre Lobo, Simon James Fong, Gloria Li, Francisco Nauber, Bernardo Gois and José Xavier Neto, “A Quantum Field Formulation for a Pandemic Propagation". In: Marques, J.A.L., Fong, S.J. (eds) Epidemic Analytics for Decision Supports in COVID19 Crisis. Springer, Cham.

7). Ivan Arraut, Alan Au and Alan Tse, “Revenue management in airlines formulated as a Harmonic Oscillator problem” (in evaluation in Physica A).

8). Ivan Arraut, Alan Au, Alan Tse and Alexandre Lobo, “On the probability flow in the stock market I: The case of the Black-Scholes equation”, arXiv:2001.00516 [q-fin.GN].

9). Ivan Arraut, Alan Au and Alan Tse, “On the multiplicity of the martingale condition: Spontaneous symmetry breaking in Quantum Finance”, arXiv:2004.11270 [q-fin.GN].

10). Ivan Arraut and Alexandre Lobo, “Economic invariant and symmetries related to the trading scenario” (Submitted for publication).   

11). Ivan Arraut, "A quantum formulation of the market equilibrium". (Submitted for publication).

12). Marques, J.A.L., Fong, S.J., Li, G., Arraut, I., Gois, F.N.B., Neto, J.X. (2022). Research and Technology Development Achievements During the COVID-19 Pandemic—An Overview. In: Marques, J.A.L., Fong, S.J. (eds) Epidemic Analytics for Decision Supports in COVID19 Crisis. Springer, Cham.


1). M. Nowakowski and I. Arraut, “The fate of a gravitational wave in de-Sitter spacetime”. Acta Phys.Polon. B41 (2010) 911-925. 

2). I. Arraut, D. Batic and M. Nowakowski, “Comparing two approaches to Hawking radiation of Schwarzschild-de Sitter Black Holes”. Class.Quant.Grav.26:125006, 2009

3). I. Arraut, D. Batic and M. Nowakowski, “A noncommutative model for a mini Black Hole”. Class.Quant.Grav.26:245006, 2009

4). M. Nowakowski and I. Arraut, “The minimum and maximum temperature of Black Body radiation”. Mod. Phys. Lett. A, Vol. 24, No. 26 (2009) pp. 2133-2137

5). I. Arraut, D. Batic and M. Nowakowski, “Maximal extension of the Schwarzschild spacetime inspired by noncommutative geometry”. J.Math.Phys. 51 (2010) 022503

6). I. Arraut, D. Batic and M. Nowakowski, “Velocity and velocity bounds in static spherically symmetric metrics”. Central Eur.J.Phys. 9 (2011) 926-938

7). Ivan Arraut, “About the propagation of the Gravitational Waves in an asymptotically deSitter space: Comparing 2 points of view”. Mod. Phys. Lett. A 28 (2013), 1350019

8). Ivan Arraut, “The astrophysical scales set by the cosmological constant, black-hole Thermodynamics and non-linear massive gravity”, Universe 3 (2017) no.2, 45

9). Ivan Arraut, “Can a non-local model of gravity reproduce Dark Matter effects in agreement with MOND?” Int. J. Mod. Phys. D 23, No. 1 (2014)

10). I. Arraut, “On the Black Holes in alternative theories of gravity: The case of nonlinear massive gravity”, Int.J.Mod.Phys. D24 (2015) 1550022

11). Hideo Kodama and Ivan Arraut, “Stability of the Schwarzschild-de Sitter black hole in the dRGT massive gravity theory”, Prog. Theor. Exp. Phys. (2014)023E02

12). I. Arraut, “On the apparent loss of predictability inside the de-Rham-Gabadadze-Tolley non-linear formulation of massive gravity: The Hawking radiation effect”. Europhys.Lett. 109 (2015) 0002

13). Ivan Arraut, “Komar energy function in the de-Rham-Gabadadze-Tolley non-linear theory of massive gravity”, Phys.Rev. D90 (2014) 12, 124082

14). Ivan Arraut, “The black-hole radiation in massive gravity”, Universe 4 (2018) no.2, 27

15). Ivan Arraut, “Path-integral derivation of black-hole radiance inside the dRGT formulation of massive gravity”, Eur.Phys.J. C77 (2017) no.8, 501

16). I. Arraut, “The graviton Higgs mechanism”. Europhys.Lett. 111 (2015) 61001

17). Ivan Arraut and Kaddour Chelabi, “Vacuum degeneracy: Multiplicity of fundamental scales”, Mod.Phys.Lett. A32 (2017) no.21, 1750112

18). Ivan Arraut and Kaddour Chelabi, “Non-linear massive gravity as a gravitational sigma model”, Europhys.Lett. 115 (2016) no.3, 31001

19). Ivan Arraut and Carlos Segovia, “A q-deformed Bogoliubov transformations”, Phys.Lett. A382 (2018) 464-466. 

20). Ivan Arraut, “The Nambu-Goldstone theorem in non-relativistic systems”, Int.J.Mod.Phys. A32 (2017) 1750127

21). Ivan Arraut, “The origin of the mass of the Nambu-Goldstone bosons”, Int.J.Mod.Phys. A32 (2018) 1850041

22). Ivan Arraut, “The dynamical origin of the graviton mass”,  Universe 5 (2019) 166.

23). Ivan Arraut, “The counting of Nambu-Goldstone bosons in a non-Hermitian field theory”, Eur.Phys.J.C 80 (2020) 9, 873.

24). Ivan Arraut, “Black-Hole evaporation and Quantum depletion in Bose-Einstein condensates”, Mod.Phys.Lett.A 36 (2021) 02, 2150006


1). M. Nowakowski and I. Arraut, “Local effects of the Cosmological Constant”, in proceeding of the International Conference on “Problems of practical Cosmology”, ST. PETESBURG, RUSSIA, 23-27 JUNE 2008, Published by THE RUSSIAN GEOGRAPHICAL SOCIETY, SL. PETESBURG, 2008, ISBN 978-5-902632-06-1

2). M. Nowakowski and I. Arraut, “LIVING WITH LAMBDA”, BRAZILIAN JOURNAL OF PHYSICS, 38 No. 3B. (2008)

3). I. Arraut, “On the Black Holes in alternative theories of gravity: The case of nonlinear massive gravity”, Springer Proc. Phys. 170 (2016) 63-68


1). Ivan Arraut, “The Planck Scale as a duality of the Cosmological Constant”, arXiv:1205.6905[gr-qc]. (Poster presentation-Nature Prize winner, in the conference Horizons for Quantum Physics, organized in Taipei, October, 2012).

IV). INDEX h: 

a). h=13 in agreement with Inspire hep: te&so=d 

b). h=13 in agreement with Google scholars: 

c). Research Gate web page:  IV


Year 1 Master
3 credits
3 credits
Year 1 Bachelor
3 credits
3 credits
2 credits
Year 2 Bachelor
1.5 credits
Year 3 Bachelor
3 credits