Dr. Jorge P. Zubelli, Professor and Chair of the Mathematics Department, recently chaired the 16th annual Research in Options: RiO 2021 conference. RiO 2021, which was held virtually from 21-24 November, provided a forum for experts to discuss some of the latest breakthroughs in mathematical research in Applied Mathematics.

This year’s meeting was co-hosted by FGV EMAp (School of Applied Mathematics in Rio de Janeiro), Universidade Federal Fluminense (UFF), Universidade Federal de Santa Catarina (UFSC) in Brazil, and KU’s Mathematics Department. Over 200 scientists, mathematicians, and practitioners who work on the interface of mathematics and finance discussed the latest research and tools that are advancing understanding of complex financial phenomena.��

The conference builds on the success of previous editions, which were hosted by Brazil’s National Institute for Pure and Applied Mathematics’ (IMPA) and the Laboratory for Analysis and Mathematical Modeling in the Applied Sciences (LAMCA), which was headed by Dr. Zubelli from 2011 – 2019.��

This year, the conference focused on different aspects of mathematical finance, including option pricing, fixed income, volatility trading, real options, commodities, algorithmic trading, portfolio and risk management.

Some of the most prominent names in quantitative finance and risk management participated in the event, including Bruno Dupire, Head of Research Bloomberg, who is recognized as one of the most influential quantitative analysts having received in 2008 the “Lifetime Achievement Award” by Risk Magazine. KU’s Dr. Giorgio Consigli, Associate Professor of Mathematics, also participated in the conference and presented on the topic of “Optimal option portfolios with volatility as asset class in a discrete market.” While KU’s Dr. Marcos Lopez de Prado, Professor of Practice in the Mathematics Department and ADIA’s Global Head on Quantitative Research & Development, presented on “Escaping The Sisyphean Trap: How Quants Can Achieve Their Full Potential.”����

The RiO conference sheds light on the increasingly important role of mathematical tools to model and understand how risk is assessed and managed, and how to address the growing number of mathematical and computational challenges the financial industry is facing.

Submitted manuscripts from RiO 2021 will be published in a special issue of the��, titled “Computational Mathematics and Data Science Methods in Quantitative Finance,” with Dr. Zubelli and two others serving as guest editors.��

Erica Solomon
Senior Publication Specialist
13 December 2021

The post KU Professor Chairs Research in Options: RiO 2021 appeared first on Khalifa University.

Editor’s Note: This article was updated on 24 November 2021

Two student teams from Khalifa University competed against more than 495 universities in the�� , investing non-fiat US$1 million in trade currency to buy and sell stocks and other commodities over the course of the 7-week competition.��

We are so proud of our KU students for participating in this challenge, which is based on a real-world investment environment using the popular Bloomberg Terminal platform.��Through their dedication and strong team cooperative spirit, and by leveraging the skills they’ve acquired from either business or math courses at KU, our teams performed extremely well and gained a strong understanding of real-world trading.

The team with Faculty Advisor Dr. Ricardo H. Archbold, Assistant Professor of Humanities and Social Sciences, includes the following members:

• Team Captain: Zehara Ali, BSc in��Biomedical Engineering
• Cidrik Mulugheta, BSc in Chemical Engineering
• Hamad Alblooshi, BSc in Mechanical Engineering
• Khalid Adam, BSc in Chemical Engineering
• Tiemar Semere, BSc in Computer Engineering

The second team with Faculty Advisor Dr. Giorgio Consigli, Associate Professor of Mathematics, and supporting advisor Dr. Jorge Zubelli, Professor of Mathematics, includes the following members:

• Team Captain: Bruno Nunes Costa, PhD student
• Omar Forrest, PhD student
• Iman Chaabi, BSc in Mathematics
• Haya Mayoof, BSc in Mathematics
• Mohammed El Amin Azz, BSc in Mathematics

At the end of the competition, Team Captain Zehara placed 50th, while Team Captain Bruno placed 77th, out of 496 total competing universities. While in the Middle East/Africa Regional competition, Team Captain Zehara placed 6th and Team Captain Bruno placed 8th. This is particularly impressive considering that most of the team members do not have a strong knowledge of finance or trading.

The students used the same type of terminals and data information that is available to real investment banks and financial exchanges.�� They gained the knowledge of how to access financial information and determine the economic trends that affect stocks and other commodities and exchanges across the world.��Profits and losses were determined by the real-world performance of these financial instruments.�� The teams had to indicate the strategy they used to determine the trades.

Participating students became certified on the Bloomberg Terminal, which gives them a competitive advantage in the job market post-graduation.

Erica Solomon
Publication Senior Specialist
9 November 2021

The post KU Students Compete in Bloomberg Trading Challenge appeared first on Khalifa University.

Mathematical equations developed by Dr. Davide Batic, Associate Professor of Mathematics at Khalifa University, predict what may be at the center of the universe is not a Black Hole, but dark matter.��

Recent advances have captured the scientific imagination, with the first image of a black hole presented in 2019 and the 2020 Nobel Prize in Physics awarded to three physicists who proved the existence of a black hole at the center of our galaxy.

Now, Dr. Davide Batic has added to this research, publishing models that show the Nobel Prize-winning conclusion could be correct, but could also be wrong.

Dr. Batic, Associate Professor of Mathematics at Khalifa University, worked with D. Asem Abuhejleh, mathematics student at KU, and Dr. Marek Nowakowski at Universidad de los Andes, Colombia. They published their results in.

Black holes form when the center of a very massive star collapses upon itself. As stars die, the nuclear fusion at their core runs out of fuel. This means the constant outward push that balanced the inward pull of gravity from the star’s own mass is gradually reduced. When there is no longer a balance, the star begins to collapse under its own mass. If it collapses into an infinitely small point, it becomes a black hole.

Roger Penrose, Reinhard Genzel and Andrea Ghez were awarded the 2020 Nobel Prize in Physics for their work in understanding black holes, demonstrating that they are an inevitable consequence of Albert Einstein’s general theory of relativity, and then finding them. While black holes’ potential existence was proved possible through general relativity, finding them was more complicated.

In 1965, Penrose used new tools in mathematics to prove that a star collapsing and turning into a black hole is possible. Then Genzel and Ghez provided the most convincing evidence to date of a supermassive black hole at the center of the Milky Way. They found that Sagittarius A*, the black hole in question, was tugging on the stars orbiting it, making them move in very unusual ways.

Their independent discoveries of a mass four million times more massive than the sun are considered the most convincing evidence of a black hole at the center of our galaxy.

“By observing the orbital motion of stars residing in the center of our galaxy, physicists determined that there must be a huge mass sitting at the galaxy core,” Dr. Batic said. “Because this feature was accompanied by other peculiarities in the star trajectories close to the galactic core, they concluded that this mass must be a huge black hole. However, we wanted to add an important aspect to their conclusion that they did not consider: the presence of dark matter in our galaxy.”

With dark matter, more is unknown than known. Dark energy comprises roughly 68 percent of the universe, with dark matter making up about another 27 percent. Everything else — every atom, every molecule, every bit of normal matter humanity has ever observed — adds up to less than 5 percent of the universe.

Unlike normal matter, dark matter does not interact with electromagnetic forces. It does not absorb, reflect or emit light, and its existence has been only inferred by the gravitational effect it appears to have on visible matter.

“Given a mass as big as the one estimated by Penrose, Genzel and Ghez, considering the star trajectories that they observed and taking into account that most matter in the universe is made of dark matter, can we always conclude that it’s a black hole at the galactic core?” Dr. Batic said. “The answer is: It depends! It depends on how you model dark matter.

“We discovered two scenarios: According to one model, there can be a fuzzy black hole at the center, while in the other model, there is no black hole at all, but a self-gravitating ultramassive object produced by dark matter itself.”

A black hole is a region of space where matter has collapsed in on itself and the gravitational pull is so strong that nothing, not even light, can escape. It is infinitely dense and can be billions of times more massive than the sun.

The edge of a black hole, the point of no return beyond which nothing can escape, is known as the event horizon, and anything that crosses the event horizon is carried toward the singularity at the center of the black hole.

Einstein’s general theory of relativity describes physics at a grand scale; however this theory breaks down when applied to what happens inside the singularity. At this point, quantum mechanics comes into play, describing nature at the smallest scales of atoms and subatomic particles. Unifying the two remains one of science’s greatest challenges.

“In theoretical physics, string theory is our best candidate theory, which brings together quantum mechanics and general relativity,” Dr. Batic said. “If we reimagine a black hole as a fuzzball, with no singularity and no event horizon but a big tangled ball of the strings of string theory, we can resolve the issue of reconciling the classical and quantum descriptions of a black hole.”

String theory says that the entire universe is made out of strings that vibrate in various complicated ways to create space, time and all the forces and particles we know. If a black hole is actually a ball of said strings, it wouldn’t look like a smooth featureless pit of gravity narrowing down to a single point, but instead a ball packed full of strings with a fuzzy surface. A fuzzball black hole would still be dense enough to affect the stars around it in the same way a conventional black hole would, with the same effects on spacetime and light, which is why Dr. Batic’s model can predict them.

However, when the model is tuned differently to include dark matter in the center of the galaxy, the outcome is very different, predicting a dark matter�� “droplet,” which is self-gravitating with no central singularity.

A fuzzy droplet has no event horizon, no exterior. If a horizon develops, it is a fuzzy black hole. A dying star may be one way of producing a black hole, but black holes may also have been formed during the Big Bang: primordial black holes made from dark matter. These would be much smaller than the black holes we know, too small to have been produced from a star, and even smaller than our sun. Primordial black holes would also form binaries, where two black holes orbit each other, which Dr. Batic’s previous work has focused upon.

For now, scientists are yet to find a primordial black hole or a fuzzy droplet. But the math works, as evidenced by Dr. Batic.

Jade Sterling
Science Writer
23 September 2021

The post Using Mathematics to Uncover the Mysteries at the Center of our Universe appeared first on Khalifa University.

Researchers at KU have used the theory of General Relativity to figure out a new way to chart our universe and possibly detect cosmic strings.��

Read Arabic story .

A team of researchers from Khalifa University has used the theory of General Relativity to figure out a new way to detect cosmic strings across the universe. The team applied the concept of ‘gravitational lensing’ to a family of pairs of black holes connected by a cosmic string in what is known as a C-metric, and computed the first ever lensing formula that can be coupled with existing technologies to chart our universe.��

Dr. Davide Batic, Associate Professor of Mathematics, Maha Alrais Alawadi, student from the Department of Mathematics, and Dr. Marek Nowakowski, Associate Professor from the Universidad de los Andes, Columbia, published their work last month in the journal.

What is gravitational lensing?

According to Einstein, the presence of a mass deforms the space-time geometry in such a way that light rays passing nearby get deflected. This is the idea behind gravitational lensing, where rays of light bend near sources of gravitation, such as stars. The greater the mass, the greater the gravity and the closer to the source of gravity, the greater the bending. This effect was observed for the first time in 1919, when English physicist Arthur Eddington measured the position of stars near the Sun before a total eclipse of the Sun and during the eclipse. By doing this, Eddington could discern if the Sun’s gravity bent the rays of light from these nearby stars.

The stars did appear to be displaced, but only by a small amount. However, this was compatible with what was predicted by Einstein’s theory of General Relativity. The mass of the Sun had caused the light to bend only at the plasma limb, or the very edge of the Sun.

“What Eddington observed was the least striking aspect of this gravitational distortion,” explained Dr. Batic. “However, scientists soon realized that this phenomenon could be used to probe the cosmic depths with an accuracy never imaged before, opening the door to modern cosmology. Gravitational lensing became and still is an extremely active research field.”

Modern technology in astronomy can measure the relative position of the stars, using this technique.

Imagine two stars and the Earth in a line: the effect of gravitational lensing would bend the light from the furthest star around the nearest star, creating a a displaced faint image of the star, which otherwise would be impossible to observe.�� If we replace the gravitational source between the Earth and the distant star with a black hole, light rays emanating from the distant star may get caught by the black hole. These rays may move around a circular orbit in the exterior of the black hole and we would observe a ring of light around the black hole. In this way, we could infer the existence of the distant and apparently hidden bright gravitational object. This hypothetical effect is what scientists call an “Einstein ring.” Since the prediction of the light bending rule of general relativity, which suggests a direct interaction between gravitation and electromagnetism, several distorted images of distant galaxies, stars, star clusters and Einstein rings have been detected by extremely sensitive telescopes. The strong evidence of gravitational lensing in the universe suggests that this technique could be used to infer the existence of black holes scattered across the universe.

Using gravitational lensing to spot black holes

Light rays passing very close to a black hole may experience very strong deviations allowing us to ‘see’ black holes whether the light source is behind the black hole (standard gravitational lensing) or in front of the black hole (retrolensing).

“Light bending and possible bound states of light are genuine effects of general relativity,” explained Dr. Batic. “Whereas light bending has been studied and even observed in a variety of situations, bound orbits of massless particles are an interesting phenomenon and they deserve special attention.”

The research team investigated the effects of gravitational lensing on two black holes in a C-metric. A C-metric describes space-time with two black holes; one black hole here in this universe and one in a parallel universe. The two black holes have equal mass and are accelerating away from each other at a constant rate as a ‘cosmic string’ pulls the black holes apart. The team realized that the black holes in a C-metric would scatter light rays in such a way that would allow for gravitational lensing to detect them.

“There are two kinds of gravitational lensing: weak and strong lensing,” explained Dr. Batic. “Weak lensing occurs when the light rays emanating from the source pass at a distance from the gravitational object in the middle. Strong lensing occurs when the light rays travel very close to the gravitational source, and particularly when close to a special distance from the object called the photon sphere.”

While weak lensing for two uncharged black holes connected by a cosmic string is too small to be detected, strong lensing would indeed work, and the team went on to calculate the formula for detecting black holes in this way.

Their computations found that a weak lensing analysis applied to a supermassive black hole or anything smaller cannot discriminate what kind of metric is being represented. However, their new equations represent the general formula for using black holes in strong gravitational lensing and can be used with observational data to confirm or disprove the existence of black holes described by a C-metric.

“In order to understand the relevance of our result, we need to remember that in theoretical physics, String Theory or the Theory of Everything is our best candidate theory which brings together quantum mechanics with general relativity,” explained Dr. Batic. “Among several predictions provided by String Theory, we also find the so-called cosmic strings. If cosmic strings are observed by means of our theoretical predictions, this would provide the first experimental evidence of a string theory model underlying the structure of spacetime.”

��

Jade Sterling
Science Writer
21 January 2021��

The post KU Research Predicts New Effect for Proving the Existence of Cosmic Strings appeared first on Khalifa University.