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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 27 open journal systems 


Malliavin Calculus in Lévy spaces and Applications to Finance.

Evangelia Petrou, TU Berlin


Abstract
The main goal of this paper is to generalize the results of Fournie et al. [7] for markets generated by Lévy processes. For this reason we extend the theory of Malliavin calculus to provide the tools that are necessary for the calculation of the sensitivities, such as differentiability results for the solution of a stochastic differential equation.


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Pages: 852-879

Published on: May 8, 2008
Bibliography
  1. Applebaum, D. Lévy processes and stochastic calculus. Cambridge Studies in Advanced Mathematics, 93. Cambridge University Press, Cambridge,2004. xxiv Math. Review 2072890
  2. Benth, F ; Di Nunno, G ; Løkka, A ; Øksendal, B ; Proske, F . Explicit representation of the minimal variance portfolio in markets driven by Lévy processes. Conference on Applications of Malliavin Calculus in Finance (Rocquencourt, 2001). Math. Finance 13 (2003), no. 1, 55--72. Math. Review 1968096
  3. Bichteler, K ;Gravereaux, J;Jacod J. Malliavin calculus for processes with jumps. Stochastics Monographs, 2. Gordon and Breach Science Publishers, New York,1987. Math. Review 100847
  4. Davis, M. ;Johansson, M. Malliavin Monte Carlo Greeks for jump diffusions. Stochastic Process. Appl.(2006),no. 1, 101--129. Math. Review 2186841
  5. Di Nunno, G ;Meyer-Brandis, T;Øksendal, B ;Proske, F . Malliavin calculus and anticipative Itô formulae for Levy processes. Infin. Dimens. Anal. Quantum Probab. Relat. Top.8(2005),no. 2, 235--258.

    Math. Review 2146315
  6. El-Khatib, Y ;Privault, N . Computations of Greeks in a market with jumps via the Malliavin calculus. Finance Stoch.8(2004),no. 2, 161--179. Math. Review 2048826
  7. Forster,B;Luetkebohmert,E;Teichmann, J. Absolutely continuous laws of jump-diffusions in finite and infinite dimensions with applications to mathematical finance. arXiv, math.PR, 2005.
  8. Fournié, E ;Lasry, J ;Lebuchoux, J ;Lions, P ;Touzi, N . Applications of Malliavin calculus to Monte Carlo methods in

    finance. Finance Stoch.(1999),no. 4, 391--412. Math. Review 1842285
  9. Johansson, M. Malliavin Calculus for Lévy Processes with Applications to Finance. PhD thesis, Imperial College, 2004.
  10. Itô, K . Spectral type of the shift transformation of differential processes with stationary increments. Trans. Amer. Math. Soc.(1956), 253--263. Math. Review 0077017
  11. León, Jorge A. ; Solé, Josep L. ; Utzet, Frederic ; Vives, Josep . On Lévy processes, Malliavin calculus and market models with jumps. Finance Stoch. 6 (2002), no. 2, 197--225. Math. Review 1897959
  12. Løkka, A . Martingale representation of functionals of Lévy processes. Stochastic Anal. Appl.22(2004),no. 4, 867--892. Math. Review 2062949
  13. Nualart, D. The Malliavin calculus and related topics. Second edition. Probability and its Applications (New York). Springer-Verlag, Berlin,2006. xiv+382 pp. ISBN: 97 Math. Review 2200233
  14. Nualart, D ;Vives, J . Anticipative calculus for the Poisson process based on the Fock space. Séminaire de Probabilités, XXIV, 1988/89, 154--165, Lecture Notes in Math., 1426, Springer, Berlin,1990. Math. Review 1071538
  15. Protter, P Stochastic integration and differential equations. Second edition. Version 2.1. Stochastic Modelling and Applied Probability, 21. Springer-Verlag, Berlin,2005. xiv+419 pp. ISB Math. Review 2273672
    16. Solé, J ;Utzet, F;Vives, Josep . Canonical Lévy process and Malliavin calculus. Stochastic Process. Appl.117(2007),no. 2, 165--187. Math. Review 2290191
  16. Yablonski, A. The Malliavin calculus for processes with conditionally independent increments. In Stochastic Analysis and Applications, volume 2 of Abel Symposia. Springer, 2007.
















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Electronic Journal of Probability. ISSN: 1083-6489