Just turned over a new leaf and became a wise and intelligent student

Chapter 392 Specialized research? No, I just read it.
"Xiao Xu, the future belongs to you. I guess I'll be seeing you win awards more often in the future."

Academician Peng seemed to only occasionally dislike Tian Gang when he was with him. When he was talking to Xu Qingshan, he was very kind.

"Academician Peng, thank you for your compliment."

When Xu Qingshan speaks out, it is either in front of acquaintances or on the stage under the spotlight.

“I still need to learn more from Academician Peng.”

"You are so polite, kid."

Academician Peng said with a smile while eating.

"I told you that we are all family. You can call me the same as you call your teacher. There is no outsider."

Academician Peng was all smiles.

A young talent like Xu Qingshan, who has a handsome appearance and great talent, can be seen at first glance to be very respectful to his teachers.

Otherwise, why do people say that old guy Tian Gang is so lucky?
He met Xu Qingshan at a time when he had the most energy to cultivate young people. Whether it was resources or development in all aspects, he was able to give Xu Qingshan sufficient guidance.

Unlike some scholars who never meet a good disciple that suits their needs until they are about to die.

In particular, Xu Qingshan also demonstrated strong mathematical ability in computers, which made Peng Shige even more envious.

You know, Lao Peng is a math expert.

His main research areas are probability theory, control theory and financial mathematics.

Academician Peng and French scholars jointly created the theory of backward stochastic differential equations, derived the nonlinear Feynman-Kac formula, and extended the traditional linear path integral to nonlinear situations. At the same time, it expanded Kolmogorov's probability theory axiom system, established the theory of nonlinear Brownian motion and stochastic analysis, deepened the probability theory system, provided a mathematical foundation for dynamic financial risk measurement, and provided key mathematical tools for pricing and risk management of financial derivatives.

This time he was invited to give a one-hour report at the International Congress of Mathematicians. The main content of the report revolved around his core research, namely the extension and realization of the theory of backward stochastic differential equations, the nonlinear Feynman-Kac formula, and the theory of nonlinear mathematical expectations. This almost represents that in the field of financial mathematics on this planet, Lao Peng has already stood in the first echelon.

If Xu Qingshan had not suddenly appeared.

Professor Peng Shiguo will be the first Chinese mainland mathematician to give a one-hour speech at ICM, which will further highlight the milestone significance of his research in the international mathematics community.

in particular.

Academician Peng was actually invited much earlier than Xu Qingshan, and the promotion began almost last year.

Of course, this kind of publicity was not what Academician Peng intended.

He is not the type of person who likes to compete for fame and fortune, but after all, he is part of the system, and he is regarded as a representative of a major school of thought, so naturally he has no way of staying out of it.

However, the number one person in China, who has been promoted for a whole year, has now been overtaken by a young junior and is now on par with him, attracting all the attention.

If it were Mr. Qiu, he would probably be unhappy again.

Fortunately, Academician Peng had no other thoughts. He only admired Xu Qingshan.

It was like he was patiently waiting for Xu Qingshan to update the way he addressed him.

"That"

Xu Qingshan hesitated for a while and spoke cautiously.

"Old Peng?"

"Ok?"

Academician Peng's eyes widened, and he turned to look at Tian Gang. The puzzlement in his eyes seemed to be asking Tian Gang: No? Is this how you, the teacher and the student, address each other?
Tian Gang smiled without saying anything and nodded.

Xu Qingshan also saw Academician Peng's expression and felt a little embarrassed.

"I'm sorry, Academician Peng, my teacher and I are used to being casual. If you..."

"It doesn't matter! Just call me Lao Peng!"

Academician Peng saw Tian Gang's joking expression and quickly agreed.

It’s not that he can’t afford to play, he just didn’t expect it.

After all, Xu Qingshan's youth is well known. At the age of 19, he is already regarded as a world-class scholar and the young scholar most likely to stand at the pinnacle of contemporary mathematics in the future.

Of course, the latter is mainly praised in China. The international evaluation of Xu Qingshan is not low, but it has not reached that level yet.

If Xu Qingshan really solved the Riemann hypothesis, perhaps this sentence would become completely applicable throughout the world.

"Then Lao Peng, I want to ask you a question."

Xu Qingshan is actually quite interested in Academician Peng’s research.

"You're so bold to ask, is it about my research?"

Old Peng benefited a lot from it.

His view is similar to Tian Gang's. Xu Qingshan should be able to win the Fields Medal this year. He may be the first native-born Fields Medal winner in China. Now he is humbly asking for advice in front of him. Let's not talk about whether Lao Peng is a face-conscious person. Who can not like Xu Qingshan's behavior? Who would not feel embarrassed?

"Yes, your theory of backward stochastic differential equations has been very effective in practical applications in the financial field, especially in the pricing of European, American and Asian options. By converting the pricing problem into a BSDE solution and combining it with Monte Carlo simulation to obtain a numerical solution, it can handle the path dependency problem. At the same time, the BSDE model can also dynamically simulate the risk correlation and return path between multiple assets, helping investors to formulate risk control strategies, especially when the market is incomplete or constrained, such as in the stage of high borrowing rate and liquidity restriction, to provide hedging solutions."

As soon as Xu Qingshan opened his mouth, Lao Peng knew that Xu Qingshan had really read his theory. He nodded with satisfaction and answered casually.

"Yes, for example, the average price calculation in Asian options. The forward and reverse joint solution characteristics of BSDE give it a natural advantage in path-dependent problems such as option pricing and complex derivatives valuation. The nonlinear mathematical expectation I proposed, namely g-expectation, expands the traditional linear framework in the BSDE model, so that when using the model for prediction, it can be more in line with nonlinear phenomena in the actual financial market, such as when market frictions and transaction costs change. It can be said that the BSDE theory is now the most valuable financial mathematical tool, and there is no other."

Mathematicians generally feel a sense of inexplicable pride when talking about their own specialized research.

Xu Qingshan and Li Guangzhi both have this emotion, and now it is even more obvious in Old Peng.

And his pride is very pure.

It's not about showing off one's own achievements, but rather like taking one's most proud son out for a walk and comparison.

If there are two people who are also talking about their own achievements, and they sit together and discuss them, it can be considered an academic cricket fight to some extent.

"Yep."

Xu Qingshan nodded and suddenly said something.

"But Lao Peng, can your BSDE make a lot of money in the Chinese stock market?"

After Xu Qingshan's words came out, the table fell silent.

Tian Gang blinked but didn't dare say anything. He stared intently at the empty plate in front of him and glanced at Lao Peng's expression.

Hey, you are worthy of being my apprentice.

Such a vulgar question can be asked. Those who know this place would say that this is the dining table of top mathematicians, while those who don’t would think that this is a conversation between scientists and social vagrants.

Although Lao Peng is friendly and down-to-earth, Xu Qingshan was the first person to raise this question in front of him.

After all, everyone who understands knows that sometimes just because a leader makes you feel down-to-earth doesn't mean you can really pull the leader down to earth. Lao Peng's status and position are no worse than Tian Gang's.

Although scholars at this academician level will not bully children, it is impossible for them to be bullied by children.

As soon as Xu Qingshan said this, Peng Shige was stunned for a while and didn't say anything for a long time.

But he was not angry. Instead, he was thinking seriously about Xu Qingshan's question.

Xu Qingshan observed Academician Peng's expression for a while, and seeing that he was not angry, he knew that they could continue the conversation, so he quietly put forward his own views.

"Lao Peng, what I mean is actually."

"The numerical solutions of BSDE, such as Monte Carlo simulation and discrete flow method, require a lot of computing resources and are much slower than traditional methods. Our current computing resources are actually quite limited. Even for supercomputing platforms, the queues are as long as the Nantianmen. But if the computing resources are limited, BSDE will have to face the problem of computing efficiency, especially in high-dimensional problems, it is very likely to face the 'curse of dimensionality'. Moreover, this computing method has a high demand for storage, which will greatly limit the application of scenarios with high real-time requirements."

Xu Qingshan paused, and seeing that Academician Peng was listening very attentively and Tian Ganglaoden's expression changed again, he continued.

"For example, our Chinese stock market."

"We are all very clear that China's stock market is not very different from other stock markets, whether they are European, American, or Asian."

"Old Peng, you should know the specific situation better than me."

"Of course, apart from this strong need for immediacy, the problem of parameter sensitivity is also not small. The model relies heavily on the accuracy of input parameters, such as volatility and interest rates. Parameter estimation bias may cause the results to deviate significantly from reality. If the stock market is stable, this kind of parameter input is fine, but when the market fluctuates violently, it is difficult to ensure that the input parameters are accurate and timely."

Tian Gang looked at Xu Qingshan in surprise as he gave a long speech in front of Lao Peng.

What is this scene like?
Showing off one's sword in front of Guan Gong and playing with mechanisms in front of Lu Ban.

Xu Qingshan took the theory that others had researched and talked about it in front of others, but this was not the most terrifying thing. The most terrifying thing was that Lao Peng's expression became more and more serious, and he listened very seriously. I don't know when he pushed away the plate in front of him, took out the notebook he carried with him, and started comparing.

What does this mean?
This means that everything Xu Qingshan said was fucking right!
No?

Haven't you been busy as hell recently? When did you start studying Lao Peng's BSDE theory?
"You are very accurate. I encountered these problems when I re-tested the theory later."

Academician Peng listened quietly to what Xu Qingshan said before he spoke slowly.

Tian Gang felt that the drink in his hand no longer tasted good.

"In fact, I find that the actual application scenarios are somewhat contradictory. If we want to quickly put our theory into practical use, we still need to simplify the model assumptions and perform calculations under the conditions of sufficient market completeness and frictionless transactions, which further weakens the practicality of the theoretical results."

"Not to mention the special situation of our Chinese stock market, where institutions enter first and retail investors wait for T+1, even when deriving fair price boundaries for stock options in Europe and the United States, it is difficult to achieve this ideal assumption."

"I have some ideas myself, but I'd like to hear your opinions now."

Old Peng looked at Xu Qingshan seriously.

Although the young man in front of him was really young and could be Lao Peng's grandson, Lao Peng still had a feeling from the bottom of his heart that he had met a soulmate.

Although it is not too difficult to understand one's own research theory under the premise that complete research has been conducted by predecessors, Lao Peng may be able to achieve this level by just picking another relatively good doctoral student.

But Xu Qingshan is only 19 years old.

He also has his own specialized research areas.

His keen understanding of financial mathematics basically made Lao Peng feel spiritually happy.

He is in a hurry now.

He was anxious to see what suggestions Xu Qingshan could come up with, so as to find a point of resonance with Xu Qingshan, and tried his best to fill this small loophole with his university knowledge.

When Xu Qingshan saw Academician Peng's attitude, he grinned.

"I think there are three main directions. The first is to develop efficient numerical algorithms, which can seek to improve the solution speed from parallel computing, deep learning acceleration, etc.; the second is to combine machine learning to optimize parameter estimation and reduce model sensitivity; the third is to try to integrate BSDE with reinforcement learning to enhance dynamic decision-making capabilities."

“In fact, it means to fully integrate the algorithm optimization advantages of machine learning into your financial mathematics theoretical foundation, so that it is easier to put it into practical application.”

The solution proposed by Xu Qingshan is very simple.

Let’s collaborate!
As for who to cooperate with?

Isn't the best candidate clearly in front of him?
Old Peng thought about it and nodded.

The three points raised by Xu Qingshan were actually part of his considerations. As a top academician, he naturally understood his research better than Xu Qingshan, and his considerations were more comprehensive than Xu Qingshan's.
"But I haven't really come into contact with machine learning. Although I know that probability theory and control theory have a wide range of applications in the field of machine learning, I don't know if I, an old man, can learn it quickly."

Lao Peng said with a smile.

Although probability statisticians can easily cross over to the field of information science, even a large number of machine learning experts are defectors with a bachelor's degree in mathematics.

But at Lao Peng's age, he feels that he may not be able to keep up with the pace of young people.

"I'm here!"

Xu Qingshan was a little anxious and spoke quickly.

"Mr. Peng, my lab has an information technology lab, and I also have multiple collaborative project groups, all in the Information Technology Center of Peking University. We have made many achievements in the field of machine learning. Take a look."

Xu Qingshan was just about to take out his cell phone to sell something when he heard Lao Peng make the final decision.

"Then I'll leave it to you! Qingshan, you were the one who asked for it."

Xu Qingshan was stunned when he saw Academician Peng showing a sly smile that he had never shown from beginning to end.

Damn it.

Who said Academician Peng is an honest man?

"Okay, since I asked you the question first, I will definitely be the one to apply for this."

Xu Qingshan knew what Academician Peng meant. This time he took the initiative to ask for cooperation, but he himself didn't really care about it.

"Then it's settled. We'll talk about it slowly tonight. I'm in a good mood today, so I'll go get some more food."

Academician Peng carried the plate contentedly and went to find something to eat.

Tian Gang, who had been holding it in for a long time, finally asked.

"Hiss, Qingshan, when did you start studying Lao Peng's topic?"

"Ah? Specialized research? No, I just looked it up."

(End of this chapter)