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BerndSchmitz
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Best Books on Stochastic Calculus

March 23rd, 2015, 8:40 am

What are your favourite Stochastic Calculus Books? I want to add something to my lonely Shreve (Stochastic Calculus for Finance II - Continious-Time Models), which I found a pretty good read. I'm looking for something mathematical clean but not too technical.Regards,Bernd
 
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Alan
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Best Books on Stochastic Calculus

March 23rd, 2015, 6:13 pm

Oksendal (Stochastic Differential Equations) is a gem.
 
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Polter
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Best Books on Stochastic Calculus

March 23rd, 2015, 7:38 pm

Like both Shreve as well as Øksendal.Other than that:* Financial modelling with Jump Processes by Cont & Tankov -- good intro to jumps* Stochastic Integration and Differential Equations by Philip Protter -- this is somewhat in the technical territory, but still think it's the reference to go to learn about semimartingales; if too step, the following notes may help along the way:- Stochastic Calculus Notes by Alan Bain- An essay on the general theory of stochastic processes by Ashkan Nikeghbali- Stochastic Calculus Notes by George LowtherSome alternatives (or complements) to Protter -- haven't had time to examine these more deeply, but parts looked interesting:- Klebaner (2005) "Introduction to Stochastic Calculus with Applications"- Meyer (2001) "Continuous Stochastic Calculus with Applications to Finance"- Bass (2011) "Stochastic Processes"By the way, would anyone happen to have any further thoughts on the above three -- say, how do they compare with the Protter's text?Edit: As for the notes, Almost None of the Theory of Stochastic Processes (a lovely title, incidentally :]) by Cosma Rohilla Shalizi with Aryeh Kontorovich also seem pretty decent -- with Part IV, "Diffusions and Stochastic Calculus," particularly relevant in our context.
Last edited by Polter on March 22nd, 2015, 11:00 pm, edited 1 time in total.
 
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Cuchulainn
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Best Books on Stochastic Calculus

March 27th, 2015, 1:23 pm

And I am sure Alan Lewis' upcoming Sto Vol book Vol II. And Thomas Mikosch' book.
Last edited by Cuchulainn on March 26th, 2015, 11:00 pm, edited 1 time in total.
 
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Orbit
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Best Books on Stochastic Calculus

March 27th, 2015, 4:48 pm

My two cents: To me, the Shreve book tries to be two things - introductory and formal - and falls in the gap between both. For example try to work the chapter problems; you'll find that the material that would explain the problems is often in a different chapter. I think it was done this way to challenge the student but often results in frustration.@PolterI've actually met Bass and he is a really nice guy, very down to earth, and really good at what he does. That said, I think there may be a struggle for a student to see the financial relevance to his Stoch. Processes book. I agree Klebaner is pretty great.Not to suck up here, but this one is priceless: "Option Valuation Under Stochastic Volatility" by Lewis. Edit: How could I forget? My all-time all-purpose for understanding...everything...is Brigo and Mercurio. But honestly the second edition is just too big. The first edition was about perfect, I think all the "smile inflation and credit" stuff should have been a separate book.
Last edited by Orbit on March 26th, 2015, 11:00 pm, edited 1 time in total.
 
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pcaspers
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Best Books on Stochastic Calculus

March 27th, 2015, 5:51 pm

what about this, isn't that _the_ standard text ?
 
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Cuchulainn
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Best Books on Stochastic Calculus

March 27th, 2015, 6:55 pm

Kloeden and Platen?
 
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Orbit
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Best Books on Stochastic Calculus

March 27th, 2015, 7:34 pm

QuoteOriginally posted by: CuchulainnKloeden and Platen?Yeah, I agree; really, really great.
 
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cosmologist
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Best Books on Stochastic Calculus

September 2nd, 2015, 4:40 pm

BerndSchmitz, Shreve, the genius, wrote the finest two volumes of pure maths(applied to finance) I have ever come across. People those who have gone through the books with seriousness, including the problems, would probably agree with me.I am looking for solutions to the problems mentioned in both the parts. Not for me, but for my kids. Expecting that one of them might try to be a quant( I tried, I failed). Have you come across the solutions anywhere?Thanks in advance. May be I will send a mail to Peter, too. By the way, from some of your posts which I have followed, I can say that your posts are worth reading. cheers
Last edited by cosmologist on September 1st, 2015, 10:00 pm, edited 1 time in total.
 
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list1
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Best Books on Stochastic Calculus

September 3rd, 2015, 2:21 pm

As an initial course Random Processes I liked A. D. Wentzell book and Chung Williams Introduction to Stochastic Integration looks good for future mathematicians
Last edited by list1 on September 2nd, 2015, 10:00 pm, edited 1 time in total.
 
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Cuchulainn
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Best Books on Stochastic Calculus

September 4th, 2015, 8:28 am

What about the many books by A.N. Shiryaev
Last edited by Cuchulainn on September 3rd, 2015, 10:00 pm, edited 1 time in total.
 
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list1
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Best Books on Stochastic Calculus

September 4th, 2015, 2:12 pm

QuoteOriginally posted by: CuchulainnWhat about the many books by A.N. ShiryaevI know only his old Probability books. They are good and also have a mathematical taste of statistical applications.
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