# Book advice on stochastic calculus for finance

#### drdoombledore

Greetings,
I am looking for a book on stochastic calculus for finance. We are using the book "Introduction to stochastic calculus Applied to finance" by Damien Lamberton and Bernard Lapeyre in our course. My problem is, the book is pretty compact and I have a hard time understanding some concepts sometimes.
For example, on viable financial markets
"Denote by * the set of all non-negative random variables X such that P(X >0)>0. Clearly, * is a convex cone in the vector space of real-valued random variables. The market is viable if and only if for any admissible strategy ..."

I also studied Shreve's book too (discrete) but couldn't find this subject, as well as some others.
My question is, if someone knows both books, can you suggest a book that covers the subjects in first one, while explaining as exhaustive as Shreve's books ?
Thank you very much.

#### rajanS

I think He’s covering some conditions for arb to be possible it seems and he might be looking for a complete state space etc. I would suggest mathematical techniques in finance-tools for incomplete markets by ales cerny that covers the topic you were concerned with. Maybe even bjorks book.

#### Vvt

Try Bingham and Kiesel's Risk Neutral Valuation

#### Razvan Ilie

Most consider Shreve's Stochastic Calculus for Finance II to be the bible of stochastic calculus. If you have done the basic discrete time stuff like binomial trees already, you can read this one even if you haven't read Shreve's first book in the series.

If you ask me, stochastic calculus (specifically Ito calculus) only really has a few important concepts you need to know that you can use for almost every finance application: Ito's lemma, martingales, Ito's isometry, Girsanov's theorem, Radon Nikodym derivative, Feynman-Kac theorem, change of numeraire. Stochastic calculus is mostly repeated usage of Ito's lemma. You can learn most of stochastic calculus without buying the book if you just read about these topics, though I recommend getting the book.

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