May 19, 2017 - unification and error control, Journal of Computational Finance 7.3. (2004): 51-86. 2 ... Financial calculus: an introduc- tion to derivative pricing.
References
Paolo Vanini Version 1 May 19, 2017
Contents 0.1 0.2 0.3 0.4
0.1
Complex Analysis Convex Analysis . Fourier Transform Stochastic Analysis
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Complex Analysis
1. Ahlfors, L., Complex Analysis, 3 ed. (McGraw-Hill, 1979). 2. Fischer, W., and I. Lieb, Funktionentheorie, Vieweg Studium Aufbaukurs Mathematik, Braunschweig, Vieweg Verlag, 1988. 3. Kreyszig, E., Advanced Engineering Mathematics, 10 ed., Ch.13-18 (Wiley, 2011).
0.2
Convex Analysis
1. Stepehn Boyd and Lieven Vandenberghe, Convex Optimization, Cambridge University Press, 2009.
0.3
Fourier Transform
1. Dym, Harry, and Henry P. McKean. Fourier series and integrals, Academic Press, (1972). 2. A. N. Kolmogorov, S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Graylock Press, Rochester, New York, 1957. 3. Lee, Roger W., Option pricing by transform methods: extensions, unification and error control, Journal of Computational Finance 7.3 (2004): 51-86. 2
0.4. STOCHASTIC ANALYSIS
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4. Lewis, Alan L. Option Valuation Under Stochastic Volatility II. Finance Press, Newport Beach, CA, 2009. 5. Lord, Roger, and Christian Kahl, Optimal Fourier inversion in semianalytical option pricing, (2007). 6. Osterwalder, Konrad. Mathematical Methods in Physics, Lecture Notes ETH Zurich, 1989.
0.4
Stochastic Analysis
1. Bass, Richard F. Stochastic processes. Vol. 33. Cambridge University Press, 2011. 2. Baxter, Martin, and Andrew Rennie. Financial calculus: an introduction to derivative pricing. Cambridge university press, 1996. 3. Billingsley, Patrick. Convergence of probability measures. John Wiley Sons, 2013. 4. Bj¨ ork, Tomas. Arbitrage theory in continuous time. Oxford university press, 2009. 5. Glynn, Peter W., Martingales, Section 10, MS& E 321, Stochstic Systems, Lecture Notes, Stanford, Spring, 2013. 6. Karatzas, Ioannis, Methods of mathematical finance. Vol. 1. New York: Springer, 1998. 7. Karatzas, Ioannis, and Steven Shreve. Brownian motion and stochastic calculus. Vol. 113. Springer Science Business Media, 2012. 8. Lamberton, Damien, and Bernard Lapeyre. Introduction to stochastic calculus applied to finance. CRC press, 2007. 9. Liptser, Robert, and Albert N. Shiryaev. Statistics of random Processes: I. general Theory. Vol. 5. Springer Science Business Media, 2013. 10. Mao, Xuerong. Stochastic differential equations and applications. Elsevier, 2007. 11. Nualart, David. The Malliavin calculus and related topics. Vol. 1995. Berlin: Springer, 2006.
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CONTENTS 12. Oksendal, Bernt. Stochastic differential equations. Stochastic differential equations. Springer Berlin Heidelberg, 2003. 65-84. 13. Protter, Philip. ”Stochastic Differential Equations.” Stochastic Integration and Differential Equations. Springer Berlin Heidelberg, 1990. 187-284. 14. Pulido, Sergio, Semi Martingales and Stochastic Integration, cmu.edu, Notes, 2011. 15. Sandmann, Klaus. Einfhrung in die Stochastik der Finanzmrkte. SpringerVerlag, 2013. 16. Shreve, Steven E. Stochastic calculus for finance II: Continuous-time models. Vol. 11. Springer Science Business Media, 2004.
