Financial Stochastic Analysis

  • Tomas Cipra


Chapter 15 deals with formulas of stochastic calculus: 15.1. Wiener Process in Finance, 15.2. Poisson Process in Finance, 15.3. Ito Stochastic Integral, 15.4. Stochastic Differential Equations SDE, 15.5. Ito’s Lemma, 15.6. Girsanov Theorem on Equivalent Martingale Probability, 15.7. Theorem on Martingale Representation, 15.8. Derivatives Pricing by Means of Equivalent Martingale Probabilities, 15.9. Derivatives Pricing by Means of Partial Differential Equations PDE, 15.10. Term Structure Modeling.


Interest Rate Stochastic Differential Equation Wiener Process Partial Differential Equation Strike Price 
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Further Reading

  1. Baxter, M., Rennie, A.: Financial Calculus. An Introduction to Derivative Pricing. Cambridge University Press, Cambridge (1996)MATHGoogle Scholar
  2. Black, F., Scholes, M.: The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654 (1973)CrossRefGoogle Scholar
  3. Duffie, D.: Security Markets: Stochastic Models. Academic, New York (1988)MATHGoogle Scholar
  4. Dupacova, J., Hurt, J., Stepan, J.: Stochastic Modeling in Economics and Finance. Kluwer, Dordrecht (2002)MATHGoogle Scholar
  5. Elliot, R.J., Kopp, P.E.: Mathematics of Financial Markets. Springer, New York (2004)Google Scholar
  6. Hull, J.: Options, Futures, and Other Derivative Securities. Prentice Hall, Englewood Cliffs, NJ (1993)Google Scholar
  7. Karatzas, I., Shreve, S.E.: Methods of Mathematical Finance. Springer, New York (1999)Google Scholar
  8. Knox, D.M., Zima, P., Brown, R.L.: Mathematics of Finance. McGraw-Hill, Sydney (1984)Google Scholar
  9. Kwok, Y.-K.: Mathematical Models of Financial Derivatives. Springer, Singapore (1998)MATHGoogle Scholar
  10. Malliaris, A.G., Brock, W.A.: Stochastic Methods in Economics and Finance. North-Holland, Amsterdam (1982)Google Scholar
  11. Musiela, M., Rutkowski, M.: Martingale Methods in Financial Modelling. Springer, New York (2004)Google Scholar
  12. Neftci, S.N.: Mathematics of Financial Derivatives. Academic Press, London (2000)MATHGoogle Scholar
  13. Pelsser, A.: Efficient Methods for Valuing Interest Rate Derivatives. Springer, London (2000)MATHCrossRefGoogle Scholar
  14. Roman, S.: Introduction to the Mathematics of Finance. Springer, New York (2004)MATHCrossRefGoogle Scholar
  15. Steele, J.M.: Stochastic Calculus and Financial Applications. Springer, New York (2001)MATHCrossRefGoogle Scholar
  16. Wilmott, P., Howison, S., Dewynne, J.: The Mathematics of Financial Derivatives. Cambridge University Press, Cambridge (1995)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Dept. of Statistics, Faculty of Mathematics and PhysicsCharles University of PraguePragueCzech Republic

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