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Background

I had a very good and bright student with some decent exposure to markets and the standard college math curriculum who got overwhelmed during a mathematical finance course due to unnecessary off-topic formalisms. In particular, the curriculum of the class was a bit misleading because it promised to follow a fairly practical book (Tomas Bjork's Arbitrage Theory in Continuous Time) as its main text, while the actual class went far beyond that, largely ignoring the text. The course spent a considerable amount of time dealing with concepts such as Radon-Nikodym derivatives, Formal Measure Theory, Filtrations, Martingales (just to name a few) which - crucially - the book only mentions as an addendum in the appendix.

Of course, there is absolutely nothing wrong with any of the topics above. It is just that my student was expecting a largely more applied class in Finance, versus a purely theoretical one in Measure Theory and Martingales.

Questions

This leads me to some questions.

  1. What is the extent to which abstract topics in mathematical finance, such as Radon-Nikodym derivaties are actually relevant to markets in the real world? Do finance instructors spend any time in the markets or do they prefer to engage in a series of endless mental gymnastics often for their own sake? (Incidentally, I am not the first one asking these questions)

  2. Is this top-down approach and over-formalism necessary? Does one really need to know Radon-Nikodym derivatives (and all their intricate details) in an introductory Math of Finance class? Especially one without any prerequisites which uses a largely informal book as its main text and which is not designed for math majors?

EDITS

  • Post shortened, following the suggestions of @Noah Schweber (Thank you!)

  • There is also a link to a chat below (thank you @roddik!). Thank you all for being constructive and respectful.

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    $\begingroup$ It is true, I think, that many texts (and, I suppose, lecturers) on the subject work at a level of generality which, while not incorrect, obscures the material. For a very advanced class, I think this can be justified...as the students ought to be able to supply their own examples and they'll need the technical details in order to move forward. But an introductory class? Well, I don't see the point. All that said, I don't think this is a good forum in which to criticize some specific professor or class. Let alone the concept of tenure and the structure of various degree programs. $\endgroup$
    – lulu
    Oct 31, 2020 at 20:32
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    $\begingroup$ In a class titled the Mathematics of Finance I would expect it to be mathematics, which is to say formal, proof based mathematics. I would certainly feel misled if it lacked rigor and abstraction. $\endgroup$ Oct 31, 2020 at 20:35
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    $\begingroup$ About 8 years ago, I meant a Woman in a book store and we got to talking. She was getting a PhD in the Mathematics of Finance. She was hoping to invest money for other people. The subject of Exxon Mobil came up. She had not heard of the company. It seems to me that if we are teaching finance at the graduate level in the United States, students should know the name Exxon Mobil. I also found out that she knew nothing about debits and credits. She had no understanding of accounting. It seems to me she did not learn finance so I do not think it is right to use the word Finance in the title. $\endgroup$
    – Bob
    Oct 31, 2020 at 20:40
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    $\begingroup$ @Pellenthor First, as I said I think the lengthy anecdote can either be shortened to a single paragraph (along the lines of "I had a hardworking student with some exposure to markets and the standard college math curriculum who got lost in a mathematical finance course due to the abstract mathematics involved. This motivated me to ask:") or even removed entirely. As to the questions, only 1,2, and 6 seem appropriate for MSE, and while there's some overlap there really are at least two distinct questions there (relationship between abstract mathematical finance and the real world, and pedagogy) $\endgroup$ Oct 31, 2020 at 20:55
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    $\begingroup$ If it's a graduate course then they should have found the motivation during their time as an undergraduate. You shouldn't be covering rudimentary material in an advanced course. $\endgroup$ Nov 1, 2020 at 2:18

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