Stochastic Calculus and Financial Applications J. Michael Steele
Publisher: Springer

One of the first techniques that need to be learnt is the application of Ito's lemma for a process with jumps. Oksendal B., (2003), Stochastic Differential Equations: An Introduction with Applications, 6th edition, Berlin and Heidelberg: Springer-Verlag. The Radon-Nikodym derivative, the Cameron-Martin-Girsanov The models presented in Financial Calculus are abstractions, and obviously any real-world application would need to address a whole range of issues not considered: the assumption of liquidity, counter-party risks, and so forth. Stochastic Calculus and Financial Applications (2003). In this post, I will try to summarize a few .. Steven Shreve's books on Stochastic calculus (Volume I + Volume II) are amazing in terms of breadth. Basic intuition is built in Volume I using a discrete-time binomial asset pricing model. Stochastic processes of importance in Finance and Economics are developed in concert with the tools of stochastic calculus that are needed in order to solve problems of practical importance. Chapter three extends this to the continuous realm, using basic stochastic calculus, Ito's formula and stochastic differential equations. Shreve, S.E., (2005), Stochastic Calculus for Finance, New York: Springer-Verlag. In Volume II, the author introduces all the concepts needed to build a financial model in continuous-time. Stochastic Calculus: A … http://www.math.colostate.edu/~estep/education/st722/outline. Elementary Stochastic Calculus With Finance in View (1999).