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

Real markets do not meet the typical .. Stochastic Modeling and Applied Probability, Vol.45, Springer-Verlag,2001. Steven Shreve's books on Stochastic calculus (Volume I + Volume II) are amazing in terms of breadth. From the reviews of the first edition: "Steven Shreve’s comprehensive two-volume Stochastic Calculus for Finance may well be the last word, at least for a while, in. Michael Steele "An Introduction to Stochastic Integration" by K.L. "Stochastic Calculus and Financial Applications" by J. [40] Ioannis Karatzas, Steven E. Random Integral Equations with Applications to Stochastic Systems. In Volume II, the author introduces all the concepts needed to build a financial model in continuous-time. Random integral equations with applications to stochastic systems. Something on numerical methods. To date, discrete stochastic calculus has found robust applications in mathematical finance and fluid dynamics. RC96: Louis B Rall and George F Corliss, An introduction to automatic differentiation, SIAM: Computational Differentiation: Techniques, Applications and Tools (1996), 1-18. One of the first techniques that need to be learnt is the application of Ito's lemma for a process with jumps. Michael Steele, Stochastic Calculus and Financial Applications,. In this post, I will try to summarize a few .. Basic intuition is built in Volume I using a discrete-time binomial asset pricing model. Stochastic calculus techniques[KS01] (such as Brownian Motion, Levy Processes[App04], Wiener Processes or the Ito Calculus[Ste03b,Ste03a]) are not the only abstraction useful in thinking about financial markets.