Introduction to Stochastic Calculus with Applications (Book Review)
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- čas přidán 28. 06. 2024
- Today's book review is, "Introduction to Stochastic Calculus with Applications" Third Edition by Fima C Klebaner.
I have been looking for a good stochastic calculus book that is not an application to finance but a book that focuses on the basic ideas of stochastic calculus. I searched online for books and read a lot of book reviews and forums trying to find something to fit this purpose. I came across this book and it received good reviews from those with strong academic backgrounds. I emailed the author who was happy to provide me a copy for review (I did receive a free copy).
What I like about the book:
The topics transition in a very logical way. Often books will jump from topic to topic while leaving gaps in how the ideas relate. This book does an amazing job at layering the ideas into a full understanding of how stochastic calculus works at an introductory level. The book also provides select solutions in the back to some of the exercises found at the end of the chapters.
The book strikes a good balance of rigor and depth with application. The book does lay out assumptions, theories, and walks through some proofs while referencing other books and papers for longer drawn out proofs. Many books specifically for quantitative finance lack listing the assumptions or gloss over them as trivial. This book clearly lists them along with reasoning on why they are required.
I really enjoyed the mix of applications/examples in the last few chapters. Finance is the main topic as it has two chapters however I found the biology chapter and examples very interesting. I like that the books focuses on building a solid foundation of stochastic calculus in the first 10 chapters and then adding examples at the end. The concept of stochastic calculus itself is challenging to understand so keeping the examples for the end reduces confusion.
Final Rating: 5/5 STARS
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Wonderfully presented! Thanks Dimitri!
You've convinced me, I ordered the book ! 👍
Hey Dimitri, Can you do a Book Review of All of Statistics by Larry Weissmann? Really love your channel. I'm starting my self learning journey of Quantitative Finance as I feel like College is just a place to have good conversation with your peers and understand the topics, I mean which College has good teaching faculty? Most of them don't. I'm about to finish my undergrad degree in physics and I'm really loving the field of finance. You are doing great work ☺️.
Dimitri, did you ever think about doing a Ph.D.? I feel like based on your drive and personality, you would find it intellectually stimulating.
I have considered it and it is always a thought in the back of my mind. It would be a large time investment but definitely enjoyable.
congratulation! these videos are the hardest to do for all the time they take to digest, but I can say they are gold! years ago myself i read Baldi's "stochastic calculus" before diving into Shreve's ii.
I don't know how you can find time to read so much beside everytjing else you do!! 👍
@Eric Laas-Nesbitt i think i bought it in amazon. still available in amazon. es at least
@Eric Laas-Nesbitt i used it as a bridge before diving into Shreve's, just to gain deeper knowledge. I did not read it from cover to cover, basically all the foundation up to Ito's formula and basic calculus. i liked it. after thaat, Shreve's book felt very accesible amd natural
I learned stochastic calculus from this book, which is the first book that I used. It made me crazy, because my supervisor required me learning stochastic calculus rigorously from it.
Have you looked at Stochastic Processes: From Applications to Theory by Del Moral and Penev? Any thoughts?
Do you recommend a full course in measure theory before picking up the book? Or specific parts of measure theory?
You will need a solid understanding of probability and measure theory. There are some great free resources though. I'll link my site which has a list of free resources including measure theory.
www.fancyquantnation.com/free
Hey Dimitri totally unrelated question to your video, but when did you learn how to play the piano with sheet music? I enjoy playing by memorization and feel, but was wondering how large the learning curve would be to follow sheet music!
The piano is actually my wife's. I did play the clarinet and learned sheet music for that as a kid. It's been a long time but I would think you should be able to pick it up within a few months.
Hi Dimitri thank you for sharing this with us most schools use Stochastic Calculus for Finance by Steve Shreve,
Yes, that is the most common texts. I actually used them during my Masters.
@@DimitriBianco garbage texts in my opinion which many will disagree with, I have worked through every problem in both texts, and imo, shreve both handwaves and doesn't properly motivate a lot of the ideas, it is far more elucidating to work through the mathematical / physicist materials and then hit the finance stuff, especially if you've experimented trading options a bit, even in simulators..
The biggest problem is how to do the last term in Itos integral.
Hi Dimitri,
Big fan of yours. Could you please complie a list of books essential for being a quant at the core with more depth and originality rather than applied finance sort of books. I m sure a lot of ppl need an answer to this question. Thanks
I will consider making a video on that. It would be fairly challenging to put together but valuable to many.
@@DimitriBianco thanks sir. One more thing is linear algebra important for quant finance, if yes then to what degree. And could you please list the most important subjects in math essential for being a quant.
@@satyaswaroop9957 that list would be very long.
Linear algebra has many application from optimization (gradient descent as an example) to vector style models which use matrices to conduct calculations of multiple regressions simultaneously.
@@DimitriBianco thanks sir. I was actually working on a linear algebra book by gilbert. I felt the computations by hand a quite tedious and i like solving calculus and probability problems than linear algebra. So just wanted to know is it okay to grasp the concept of linear algebra and use scipy for finding LU, inverse, elimination matrix etc or should we be good with it by hand
Hy dude I am a second semester Physics student and I am in calc 2 as of now. Next semester I wanted to pick up statistics for scientist and engineers would u think that amount of math would be enough to start with stochastic or I need to know Multivatiable calc.
Are you familiar with Stochastic Differential Equations by Bernt Oksendal? If yes, would you recommend it?
No, I'm not familiar with Oksendal. I've heard good thing about it however I have heard it is more focused on details.
This book is alright, but I would recommend it as a start to the journey. I have a few other intro recommendations to get over the initial hurdle, but in my opinion, a full working of Rene Schillings text and Oskendals text are necessary if you want to get into advanced and full blown quant topics like infinitesimal generators, levy-type processes, malliavin calculus, and most importantly, unique volatility and risk modelling approaches, i.e. variance-gamma process for option pricing with a subordinated process for volatility (where the time change for the volatility is random itself), or fractional fokker-planck for it's memory kernel and uses in automated high frequency trading.
I also encourage people to go down the statistical physics / non-equilibrium statistical mechanics rabbit hole while internalizing and building comfort with stochastics. Both path integral approaches and diffusion/fokker-planck/statistical field theory can be insanely useful, and it is beyond enlightening and comforting to start to see the deeper connections to physics, especially ubiquitous things like 1/f noise, power laws, critical exponents, etc etc, all of which Mandelbrot was very fond of and wrote a few texts on. At the deepest level, it is comforting when you start to see the connections mathematical physics has to stochastic calculus, specifically with the supersymmetric theory of stochastic dynamics and sigma model, and it's use in quantum field theories with respect to renormalization groups and gradient flows. Nature is very stochastic, and I think becoming comfortable with that and learning the physical models, i.e. fokker-planck and diffusion and heat equation, give an insanely strong advantage to intuiting how to model financial systems and risk / option pricing models and automated trading where you need to use signal analysis, stochastic control and other techniques to analyze order book data and assess the potential market impact of various orders, and then ultimately act on this in stochastic optimal control regimes.
I would agree with adding Schillings and Oskendals however they should be reviewed after Klebaner. While the deeper you go the more beautiful the math and theory becomes, it is important to keep in mind that finance is a social science and does not play as nice as hard science like physics.
@@DimitriBianco I agree, but new fields like ambit stochastics and mean field game theory / mean field theory are finding excellent applications in both the social sciences and financial systems. The U of T prof local to where I'm at / studied at is quite advanced with HFT and mean field game theory / stochastic optimal control, see : sebastian.statistics.utoronto.ca/
@@DimitriBianco One example of where statistical physicist techniques really shine is considering the orderbook interactions, and the flow of information in the database that is an order book. The interactions are not independent, and do have varying autocorrelations / dependencies to past order book data (orders placed/cancelled, executed orders, etc), this is the sort of thing physicist in non-equilibrium statistical mechanics have done beautiful work over the decades creating models and structure around, i.e. the fractional fokker-planck / fractional diffusion equation now has a memory kernel, so you don't have to just look at the time evolution of something subjected to random forces without considering the past dependencies.
@@JaGWiREE I'll have to take a look at some of his work.
Dimitri, I don't know what your personal situation is, but please have a child. Good brains need to be passed on. Thank you for considering it.
I have a 6 month old daughter and a wife that's smarter than myself.
@@DimitriBianco Thank goodness! Good for you, happy new year, keep up the great content. BTW, Singaporean math is a great way to start her on her math journey to become the next Quant in the family!
How does it compare to Shreve?
I find Shreve's too focus on finance and less rigorous. It really depends on your goal. If you want to deeply understand stochastic calculus it will take a few books and a lot of time. If you are just wanting the basics of derivatives, then Shreve's is a better book.
I am a mathematician working in, and with a great interest in financial mathematics and stochastic calculus.
This book was one of the first I got.
To me it is one of my least favourites even if its got its merits.
The writing is clear and it covers a lot of topics. But to me, a huge problem is that it just skips too much essential proofs. This easily makes you believe thst you know things you really don't.
Yes, I know, an introductory book cannot cover too much advanced proofs and material.But I feel this book is going the wrong way about it. It is trying to cover a lot of rather advanced material, but skipping most of what is required to really understand it making it feel like a long listing of advanced results without too much explanaitions or intuition behind it.
In my opinion, a better introductory book should not try to list and say everything as quickly as possible, but rather go deeper in the intuitive explanations making the beginner grasping what is really going on.
For that purpose I liked Shreves Stochastic calculus in continuous time (book II) better. Sure, it is sloppy with the harder math, but explains intuitively what is going on in a good way, I think.
2 questions.
First, do I need to know R or Python to actually understand stochastic calculus?. Im studying math but I havent taken R or Python just yet.
Second, as you were flipping through the pages I noticed Brownian motion, Random walk, blah blah but i also saw PDEs. So on that note, i wanted to ask you to review Partial Differential Equations for Finance: Explained. I seen many quants swear by that book, even professors from the financial math masters program at my school.
You don't need any programming to understand stochastic calculus. You will need a strong understanding of calculus and probability theory though.
I'll try and take a look at that book. You'll need to understand ODEs and PDEs for stochastic calculus.
@@DimitriBianco thank you
Which is the author please? Is it, Karel in t Hout?
@@mktsp2 yes
What level of math knowledge do I need to have to be able to process what’s in that book?
Quantum physics
full calc progression, background in probability theory, measure theory. which means probably some real analysis too.
Eathan's answer is right on. To clarify on calculus progression, you need calculus 1, 2, and 3.
@@DimitriBianco business background but I’ve got calc 1-3 and probability classes. You think this would be a challenge without any real analysis?
I want to burn through this book. I should be able to learn it rather quickly. I know measure theory, I'm really good at computations in vector, tensor calc, ode, I know only very basic statistics. The problem for me is obtaining the book and finding time to read it. But, read it I shall!
To those wanting to read it: Looking at the inside of the book (time stamp 9:00), looks like you definitely need some real analysis (like in Rudin's book) background.
Rudin gives me chills, Real analysis requires a lot of work.
It is also theft from the author who spent hundreds of hours writing these books.
@@DimitriBianco lol some authors leak the PDFs themselves because springer-verlag is pure cancer
@@DimitriBianco you're not wrong, but what if you are younger and don't want to spend on buying the books?
@@ryan_chew97 Youth isn't really an excuse for theft......
Kindly review these two books 📚 inspiring
* Higher Is Calling
* Just eat the worm 🐛 by Maxwell A.
Happy New Year. 🎊
Hey Dimitri, thank you for the review.
Can you review ‘Introductory Econometrics for Finance’ by Chris Brooks?
I believe many European programs use this text in their programs but I haven’t seen many uses of it in the US.
I will consider it. Besides the trouble of getting the book, a review can take me between 3-6 months.
I could not personally learn from the text as I thought it lacked sufficient motivation and felt like I was just being thrown concept after concept. Shreve II felt like a much better, digestible text for me. Although I am not done with Shreve it feels like a much better text for what I want and what my skillset is.
The author of this text states that calculus (and Probability?) is all that's required to read the text I do not think this is entirely honest. A certain level of sophistication is required to learn this subject in general as it is difficult regardless the book. This sophistication is not as much a requirement for Shreve's text which renders it much more digestible.
Both of Shreve's books are good given you are only wanting a finance perspective. His book is typically used as the intro book for stochastic calculus to finance for many masters programs. Klebaner's book is designed for learning stochastic calculus as a general topic. To be able to apply stochastic calculus at a deeper level I find Shreve's a bit terse as the focus is only finance. Starting with Shreve's and then moving towards Klebaner is a good way to learn however you do need a math background (specifically probability theory).
@@DimitriBianco good idea I'll definitely try klebaner again after shreve!
I'm mostly interested in stochastic calculus, but Shreve seemed easiest.
Peace be upon you. Please send me books related to the subject. Thank you.
Too bad that Amazon doesn't have a Kindle digital version of this 3rd edition unlike the 2nd edition.
Who reads textbooks over kindle anywayss, I find it so weird
@@ajwadjaved9909 I do for like 8 years by now. I wouldn’t ever buy a new book in paper: it is logistically insane, and for large textbooks the size and weight are huge barriers to reading it through.
@@alex_8704 I guess yeah, I read all of my books/novels over Kindle but I just cant read textbooks over there. The page size is too small, I prefer reading textbooks over PDF with a physical notebook at my side.
@@ajwadjaved9909 It probably depends on the subject: tables can be rendered not perfectly on an iPad screen. But in other respects, if the textbook consists predominantly of text, I find it convenient that I can switch from iPad to iPhone in places where there's not enough space to hold an iPad, like in a line, on a peak-hour subway train. After all, they don't usually sell non-free books in the PDF format.
If the textbook is really long, I must confess to myself that either I read it through like that, commuting, or not read it completely at all :-(
this book is not at all rigorous. if you want something hard core try karatzas
Even he says its not that hardcore, it is a introduction book after all (: