Stochastic Calculus Book for Actuaries

[pbunyan]

Sorry to add to the plethora of "recommend me a book" posts, but I'm getting desperate after trying a few titles myself and having problems with them being too theoretical or not having a thorough solutions manual. Can anyone recommend a good book with which I can teach myself stochastic processes and very basic stochastic calculus? Preferably the book will be as un-theoretical as possible and have a solutions manual so I can check my work and not feel as if I'm crawling around in the dark. The kinds of questions I need to be able to answer are like the following: https://www.soa.org/globalassets/assets/files/edu/2021/fall/exams/fall-2021-exam-qfiqf.pdf


(For some background, I'm an actuary and I am beginning my fellowship study with the Society of Actuaries taking their quantitative finance and investments track. The contents of the track are not nearly as technical/mathematical as would be required for a quant. But, some of the exams assume previous knowledge of basic stochastic processes and basic applied stochastic calculus - strongly emphasizing their applications in financial modeling. The questions deal with the topic at a beginner-to-intermediate level with a few practical calculation type problems. I have a bachelor's in mathematics with a solid understanding of basic probability theory, but I've never studied stochastic processes or stochastic calculus so I need a speedy-ish way to learn the topics enough to answer basic questions).

 

[PepeQuant]

stochastic process is nothing more than just a a sum of random variable (as increments).

Given you have solid understanding of basic prob, i would suggest you to stick it through Shrev's book. You can try not to pay much attention to chapter 1 & 2 (just read it to get the idea of why they define probability space in such way. honestly to me it is just to describe the information at given time & events associated with it mathematically), but really starting focusing on chapter 3.

If you still not be able to do it, then most likely you miss some numerical skills. I would suggest review your calculus/ODE classes.

 

[Quasar Chunawala]

stochastic process is nothing more than just a a sum of random variable (as increments).

Given you have solid understanding of basic prob, i would suggest you to stick it through Shrev's book. You can try not to pay much attention to chapter 1 & 2 (just read it to get the idea of why they define probability space in such way. honestly to me it is just to describe the information at given time & events associated with it mathematically), but really starting focusing on chapter 3.

If you still not be able to do it, then most likely you miss some numerical skills. I would suggest review your calculus/ODE classes.

Hey @PepeQuant,

I didn't slot my time well, earlier, so haven't read Shreve.

But, I have begun reading: A first course in Stochastic Calculus. It felt like a very nice applied and practical book for a first read, with basic results proven. What do you think of this particular one?

Quasar.

 

[Daniel Duffy]

stochastic process is nothing more than just a a sum of random variable (as increments).

That description is not even wrong.