1 hour on the Platform

Last Monday I listened to Peng's (Peng Shige) Lecture about the measure of financial risks. Similar to previous lectures, there are numbers of official news reports. However, I'd like to share my personal feeling with you.

I have no better choice but to admit that Prof Peng is really an authority, not only because of his great contribution to the professional field of mathematics and finance, but also for his zeal of research and the wonderful explanation of his thought.  He has the ability to make the only an hour's lecture magic, to lead us fall in love with his "nonlinear expectation operator". It is a pity for me that after having stayed for numerous years in SDU, I know nothing about Peng's research. I think without long time precipitation of thought, it is impossible to have such deep realizations.

One word he mentioned that night really impressed me, it was: dirty work. Nowadays there are so many dirty works that make us apathetic.

Today I have said too much just because last Wed's afternoon I had an exercise class of intermediate microeconomics for one hour as a TA. I was confident about my knowledge of micro economic theory, since I could understand the book called "microeconomic theory " by Mas-Cololl,Winston,Green as least. But when illustrate these with my words and make them clear to the audience, I learned the hardness of the process. I spent more than 5 hours in front of my computer on making the handout. Since pictures were helpful, I installed Illustrator and Flash to make the visual effects better. I was willing to use these as supplements to help them understand the economic thoughts behind the mathematical formulas. Although time is needed to examine whether I have succeed, I'll work on. Personally speaking, intermediate microeconomics is too important for the whole development of the economic study.  At least, I have already achieved my initial goal, which is also the reason I used to persuade my advisor to leave me this chance: to examine my knowledge of intermediate microeconomics.

The next class will be two weeks after, and I have to work hard to prepare. I just hope that my advisor won't be disappointed about his decision and trust, and also for those who take time to attend the class it is worthy that time. At last, I have no excuse to fail. It is really worthy that much.
In the end, and also on the one-year's memorial day, I want to speak out these words: I'll do whatever in return to your guidance.

Thank you so much, dear Yue, my advisor.

[NEW] You can download all presentations here: http://www.cloudlychen.net/papers.html#impre

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How to show latex formulas on your blog/webpage/wordpress

For most people who are familiar with latex, we are addicted to the grammar of latex's mathematical formulas. However, although we can do well in PDF files, we can do little on traditional media like web pages (html) or our blog.

Fortunately, as the demand of it, some talent people provide the powerful tool. Like wikipedia, you can see the pictures  of these formulas directly and if you copy and paste them, you may get the latex code in your latex editor. Specifically, if you are using Lyx like me, you can see the formula as soon as you paste it in the mathematical environment like "equation". How cool it is!

But the fact is, what can we do on our blog? After searching for a while, I have found several solutions and tried one by one.

  • the best way is to install latex service on your servers. According to here, you can download  LatexRender. Then for those who are wordpress users, you can use the plugin WP LaTeX. Done!
  • But for those who are using third-part server like me, it is impossible to install latex service. From HERE: we can use John Forkosh's , can insert "real math images in html documents”. You only need to add latex code behind mathtex.cgi? and then you will get the image.
  • But don't you feel that it is inconvenient? You must enter the link by keyboard every time. Fortunately we have a wordpress plugin Latex for WordPess ( MimeTex for wordpress & bbPress，from here ). After the installation, it will automatically convert latex codes into gif images and cache them on your blog.

Note: Maybe you will fail to open your web pages after installing latex for wordpress. Then you may try to edit the plugin:

find this line:

class mimetex {

and then replace the following two lines with

var $server = “http://www.bytea.net/cgi-bin/mimetex.cgi?formdata=”;
var $img_format = “gif”;

Thanks for http://www.bytea.net/ and its public cgi.

Stochastic calculus [4th week, Sep]

Today when I was checking my emails, I noticed one ad from The Wharton School of the University of Pennsylvania. There was no doubt that it is the most famous business school throughout the world.  But in fact, at the first glance, I didn’t realize that it is Wharton. I just thought that “oh, a school of Upeen“.

Followed its link, I was redirected to its official website, and read the introduction of its applied economics doctoral program. Although I did know that upeen would never give me an admission, I still looked carefully at the details of the program’s requirements. Of course, I paid much attention on the mathematical requirements. Some familiar words came into view, like

(1) at least two courses in calculus, (2) linear algebra, (3) differential equations, and (4) probability and statistics. We also recommended that you have taken: (1) real analysis, (2) econometrics, (3) stochastic calculus.

Ok… I have one year left to meet your requirements. However, the fact is, even if I can satisfy all the basic requirements of this program, I am still not competitive enough and I have no money to pay for the tuition. Thus, the final result mentains the same: It has nothing to do with me. Moreover, I would prefer the training of theoretical economics rather than applied economics.

Here I want to say something about “stochastic”. Some days ago one junior attracted my interest, not for his intelligence, but for his love of mathematics as a student of economics. I had met hundreds of schoolmates who had a good knowledge of math, either took some classes from the school of mathematics or taught themselves. But most of them were forced to enhance their math ability by the pressure from graduate schools or their advisors. Therefore, the real situation was, they did have some calculation skills after professional math trainings, but seldom did they really have the understanding of the spirit of math.

That boy was different. He didn’t got high marks in every class, thereby losing the most valuable testimony of outstanding performance at study. “The only choice for me is to take part in the entrance exams for postgraduate schools ( which is called ‘Kao Yan’) since my lack of English and GPA “, he laughed at himself when I encouraged him to go abroad. But he told me that he had audited most of the core courses in school of math. That day we talked about a question about matrix, or more specifically, Markov chain. He offered a new solution way, which was really out of my thought. I didn’t catch his meaning at first, so he explained it patiently. After that, he recommended me to listen to the course of stochastic process in school of math. To speak honestly, I had some knowledge about stochastic process so I told him. At first he was a little surprised, but soon he gave me an advice for the reason that my understanding of stochastic was not deep enough. Then he gave me a list of the courses and asked whether I would come to the class or not. Unfortunately, the time was conflicted with an other class on Tuesday afternoon. He said that it didn’t matter, since I would go to another half  of the course on Thursday and the course was pretty easy. OK, I will certainly do that.

Of course, as an exchange, I provided some suggestion for the economic courses…

Now what I want to say is, why “stochastic” is so important in economics? It seems that every one has an unique answer, so do I. But today the word “stochastic calculus” really makes me confused. After searching on the Internet, I have a basic conception of it. But why it sounds so familiar? …

Yes, Shige Peng （彭实戈）! And his backward stochastic differential equations! I see… I see…

Appendix:

Some Chinese materials about Stochastic calculus ( Author unknown, sorry! ).

Continue reading in Chinese »

NO.11 Uncertainty, demand elasticity and price determination

Agriculture and modern industry are different from each other in many aspects. Here I use the supply-demand analysis as below.

On one hand, the supply of agricultural productions, such as rice and corn, is heavily relied on environmental conditions like temperature, rain and wind etc. On the contrary, the supply of industrial productions is always steady, or it is only determined on the input of raw materials. Although technology is vital, we can ignore it here since it plays an important role on both (or it will be considered later because it will also influence the degree of uncertainty).

On the other hand, the demand of food (agricultural productions) is always stable, or we can say that the price-elasticity is small, while the demand-elasticity of industrial productions is much bigger. Thus, the most interesting thing is that there is significant difference between them both in the supply and demand side, and if we also take the service-industry into account, this question will become more and more complex and interesting.

Under the traditional assumptions, we usually consider the industry as the typical model, then establish a general equilibrium model. It is reasonable because modern industry make the largest part of GDP. But at the same time, since the uncertainty of output is very limited, there is no need to waste too much on supply analysis. Therefore, we usually ignore the role of uncertainty which do exist in the real world.
Here, I wonder that if we apply this method to the economic analysis of developing or undeveloped countries, where agriculture is still very important in national production, there may be some unrealistic expectations derived from this simplified model.

So if possible, can we make a consideration of uncertainty as well? Maybe a simple way is to assume that var(output) doesn't equal 0. I don't know how to go further, but I think the results will be certainly interesting, especially in the price-determination and equilibrium, and may also be meaningful for policy-makers.