Chaos expansions and malliavin calculus for levy processes

Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito

Volumn , Issue , 2007, Pages 595-612

  Sole, Josep Lluís ^a   Utzet, Frederic ^a   Vives, Josep ^a  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; RANDOM PROCESSES; STOCHASTIC SYSTEMS;

CHAOS EXPANSIONS; LEVY PROCESS; MALLIAVIN CALCULUS; REPRESENTATION FORMULAE; SQUARE INTEGRABLE;

CALCULATIONS;

EID: 68749092738     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-70847-6_27     Document Type: Conference Paper

References (28)

1. Applebaum, D., Lévy Processes and Stochastic Calculus. Cambridge University Press, Cambridge (2004).
2. Benth, F. E., Di Nunno, G., Løkka, A., Øksendal, B. and Proske, F., Explicit representations of the minimal variance protfolio in markets driven by Lévy processes. Mathematical Finanace 13 (2003) 55-72.
3. Davis, M. H. A. and Johanson, M. P., Malliavin Monte Carlo Greeks for jump diffusions. Stoch. Proc. and their Appl. 116 (2006) 101-129.
4. Dellacherie, C. et Meyer, P. A., Probabilités et Potentiel. Theorie des Martingales. Hermann, Paris (1982).
5. Dellacherie, C. et Meyer, P. A., Probabilités et Potentiel. Processus de Markov (fin). Compléments de calcul stochastique. Hermann, Paris (1992).
6. Di Nunno, G., Øksendal, B. and Proske, F., White Noise Analysis for Lévy processes. Journal of Functional Analysis 206 (2004) 109-148.
7. Di Nunno, G., Meyer-Brandis, Th., Øksendal, B. and Proske, F., Malliavin calculus and anticipative Itô formulae for Lévy processes. Preprint series in Pure Mathematics, University of Oslo (2004) 16.
8. Itô, K., Multiple Wiener integral. J. Math. Soc. Japan 3 (1951) 157-169.
9. Itô, K., Spectral type of the shift transformation of differential processes with stationary increments. Trans. Am. Math. Soc. 81 (1956) 252-263
10. Lee, Y.-J. and Shih, H.-H., The product formula of multiple Lévy-Itô integrals. Bull. Inst. Math. Acad. Sinica 32 (2004) 71-95.
11. Lee, Y.-J. and Shih, H.-H., Analysis of generalized Lévy white noise functionals. Journal of Functional Analysis 211 (2004) 1-70.
12. Leon, J., Solé, J.L, Utzet, F. and Vives, J., On Lévy processes, malliavin calculus and market models with jumps. Finance and Stochastics 6 (2002) 197-225.
13. Løkka, A., Martingale representations and functionals of Lévy processes. Preprint series in Pure Mathematics, University of Oslo (2001) 21.
14. Ma, J, Protter, P. and San Martin, J., Anticipating integrals for a class of martingales. Bernoulli 4 (1998) 81-114.
15. Meyer, P. A., Un cours sur les integrales stochastiques, In: SÚminaire de ProbailitÚs X, Lecture Notes in Mathematics, 511, 245-400, Springer, New York, 1976.
16. Nualart, D., The Malliavin Calculus and Related topics. Springer, Berlin (1995).
17. Nualart, D. and Schoutens, W., Chaotic and predictable representation for Lévy processes. Stochastic Processes and their Applications 90 (2000) 109-122.
18. Nualart, D. and Vives, J., Anticipative calculus for the Poisson Process based on the Fock space. In: Séminaire de Probabilités XXIV (Lecture Notes in Mathematics, 1426), Springer, Berlin Heidelberg New York: Springer 154-165 (1990).
19. Nualart, D. and Vives, J., A duality formula on the Poisson space and some applications. In: Proceedings of the Acona Conference on Stochastic Analysis. (Progress in Probability). Birkhäuser (1995).
20. Neveu, J., Processus Pontuels. In: École d'Eté de Probabilités de Saint Flour, VI, (Lecture Notes in Mathematics, 598), Springer, Berlin (1977).
21. Øksendal, B. and Proske, F., White Noise of Poisson random measure. Potential Analysis 21 (2004) 375-403.
22. Picard, J., On the existence of smooth densities for jump process, Probab. Theory Relat. Fields 105 (1996) 481-511.
23. Privault, N., An extension of stochastic calculus to certain non-Markovian processes Preprint 49, Universite d'Evry, (1997) http://www.maths.univeevry.fr/prepubli/49.ps.
24. Sato, K., Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999).
25. Schoutens, W., Stochastic Processes and Orthogonal Polynomial, Lecture Notes in Statistics, 146, Springer, New York, 2000.
26. Solé, J., Utzet, F. and Vives, J., Canonic Lévy process and Malliavin Calculus. Stoch. Proc. and their Appl., to appear (2006).
27. Solé, J., Utzet, F. and Vives, J., Quadratic hedging of Asian options in jump diffusion models via Malliavin Calculus. Preprint (2006).
28. Yablonski, A., The calculus of variations for processes with independent increments, Rocky Mountain Journal of Mathematics, to appear (2006).