Need some advice for buying stochastic calculus textbook (Math student).

[ThaiMathDude]

Hi guys, I'm 1st year M.Sc student in mathematics with following background:

- Analysis: Baby Rudin, Folland, Kreyzig (Intro to functional analysis)
- Topology: Munkres, Kelley
- Probability theory: Billingsley
- Mathemaical Statistics: Casella and Berger

Now I'm interesting in stochastic calculus and find that there are many excellent textbooks on these subject such as Chung and William Vol.I-II, Karatzas and Shreve, Revuz and Yor etc. Please give me some advice to buy one of them or suggest me others if you have better choices. I need the book which is rigorous but readable relatively to my background. Thanks in advance for the advice.

P.S. This is my first thread for this forum. I'm sorry for my poor English usage.

 

[bigbadwolf]

Chung and William Vol.I-II, Karatzas and Shreve, Revuz and Yor etc

Haven't seen Chung and Williams. Karatzas and Shreve and Revuz and Yor are standard monographs on stochastic analysis but turgid to read. Karatzas and Shreve is maybe a bit easier than Revuz and Yor. If you're talking from the viewpoint of finance, these books are going way too far and way too deep. You probably want something simpler -- something like Wiersema or Klebaner. Or Shreve's two volumes.

 

[ThaiMathDude]

Haven't seen Chung and Williams. Karatzas and Shreve and Revuz and Yor are standard monographs on stochastic analysis but turgid to read. Karatzas and Shreve is maybe a bit easier than Revuz and Yor. If you're talking from the viewpoint of finance, these books are going way too far and way too deep. You probably want something simpler -- something like Wiersema or Klebaner. Or Shreve's two volumes.

Thanks for advice
I'll look on Klebaner and Shreve's two volumes. They're available for borrowing at my university library.

 

[Daniel Duffy]

Mikosch is the most accessible. Then Ubbo Wiersema.

https://www.quantnet.com/threads/is...-course-suitable-for-me-please-comment.15316/

 

[ThaiMathDude]

Mikosch is the most accessible. Then Ubbo Wiersema.

https://www.quantnet.com/threads/is...-course-suitable-for-me-please-comment.15316/

I used to skim on Mikosch and I found that I was a bit unfamiliar with Mikosch's style since I prefer definition-theorem-proof expositions (with some remark on their intuitions behind, but not too wordy to grasp the idea conveniently). Anyway, thanks for your advice

 

[bigbadwolf]

... I prefer definition-theorem-proof expositions ...

In that case, also take a look at Sean Dineen's Probability Theory in Finance.

 

[Daniel Duffy]

In that case, also take a look at Sean Dineen's Probability Theory in Finance.

I used to get some lectures from SD in the 70's.

 

[Daniel Duffy]

I used to skim on Mikosch and I found that I was a bit unfamiliar with Mikosch's style since I prefer definition-theorem-proof expositions (with some remark on their intuitions behind, but not too wordy to grasp the idea conveniently). Anyway, thanks for your advice

Mikoscjh would

I used to skim on Mikosch and I found that I was a bit unfamiliar with Mikosch's style since I prefer definition-theorem-proof expositions (with some remark on their intuitions behind, but not too wordy to grasp the idea conveniently). Anyway, thanks for your advice

Once the theorems are known, what's next?

 

[ThaiMathDude]

Mikoscjh would



Once the theorems are known, what's next?

Maybe applications or some remarks on their intuitions, I guess.

 

[Daniel Duffy]

Maybe applications or some remarks on their intuitions, I guess.

SDEs in finance.