Geodesic
Classification of Lévy processes with parabolic Kolmogorov backward equations
Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 3, pp. 525-552 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{TVP_2015_60_3_a5,
     author = {K. Glau},
     title = {Classification of {L\'evy} processes with parabolic {Kolmogorov} backward equations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {525--552},
     year = {2015},
     volume = {60},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2015_60_3_a5/}
}
TY  - JOUR
AU  - K. Glau
TI  - Classification of Lévy processes with parabolic Kolmogorov backward equations
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2015
SP  - 525
EP  - 552
VL  - 60
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TVP_2015_60_3_a5/
LA  - en
ID  - TVP_2015_60_3_a5
ER  - 
%0 Journal Article
%A K. Glau
%T Classification of Lévy processes with parabolic Kolmogorov backward equations
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2015
%P 525-552
%V 60
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_2015_60_3_a5/
%G en
%F TVP_2015_60_3_a5
K. Glau. Classification of Lévy processes with parabolic Kolmogorov backward equations. Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 3, pp. 525-552. http://geodesic.mathdoc.fr/item/TVP_2015_60_3_a5/

[1] Abramovits M., Stigan I., Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, Nauka, M., 1979, 830 pp. | MR

[2] Barndorff-Nielsen O. E., “Exponentially decreasing distributions for the logarithm of particle size”, Proc. {R}oy. {S}oc. Lond. A, 353:1674 (1977), 401–419 | DOI

[3] Belomestny D., Panov V., “Estimation of the activity of jumps in time-changed {L}évy models”, Electron. J. Statist., 7 (2013), 2970–3003 | DOI | MR | Zbl

[4] Bensusan A., Lions Zh.-L., Impulsnoe upravlenie i kvazivariatsionnye neravenstva, Nauka, M., 1987, 597 pp.

[5] Böttcher B., Schilling R., Wang J., “Lévy-type processes: construction, approximation and sample path properties”, Lecture Notes in Math., 2099, 2013, 1–199 | DOI | MR | Zbl

[6] Eberlein E., Glau K., “Variational solutions of the pricing {P}{I}{D}{E}s for {E}uropean options in {L}évy models”, Appl. Math. Finance, 21:5 (2014), 417–450 | DOI | MR

[7] Eberlein E., von Hammerstein E. A., Seminar on Stochastic Analysis, Random Fields and Applications IV, Progr. {P}robab., 58, Ed. by R. C. Dalang, M. Dozzi, and F. Russo, Birkhäuser, Basel, 2004 | MR

[8] Eskin G. I., Kraevye zadach dlya ellipticheskikh psevdodifferentsialnykh uravnenii, Nauka, M., 1973, 230 pp. | MR

[9] Glau K., Feynman–Kac–Darstellung zur Optionspreisbewertung in Lévy-Modellen, PhD thesis, Universität Freiburg, 2010 | Zbl

[10] Glau K., Feynman–Kac formula for Lévy processes with discontionuous killing rate, arXiv: 1502.07531

[11] Hammerstein E.-A., Generalized Hyperbolic Distributions: Theory and Applications to CDO Pricing, PhD thesis, Universität Freiburg, 2010

[12] Hilber N., Reichmann N., Schwab C., Winter C., Computational Methods for Quantitative Finance. Finite Element Methods for Derivative Pricing, Springer, Berlin, 2013, 299 pp. | MR | Zbl

[13] Jacob N., Pseudo-Differential Operators and Markov Processes. V. II: Generators and their Potential Theory, Imperial College Press, London, 2002, 453 pp. | MR

[14] Matache A.-M., Nitsche P.-A., Schwab C., “Wavelet Galerkin pricing of American options on Lévy driven assets”, Quantitative Finance, 5:4 (2005), 403–424 | DOI | MR | Zbl

[15] Matache A.-M., Schwab C., Wihler T. P., “Fast numerical solution of parabolic integrodifferential equations with applications in finance”, SIAM J. Sci. Comput., 27:2 (2005), 369–393 | DOI | MR | Zbl

[16] Matache A.-M., von Petersdorff T., Schwab C., “Fast deterministic pricing of options on {L}évy driven assets”, Math. Modell. Numer. Anal., 38:1 (2004), 37–71 | DOI | MR | Zbl

[17] Picard J., “On the existence of smooth densities for jump processes”, Probab. Theory Related Fields, 105:4 (1996), 481–511 | DOI | MR | Zbl

[18] Poirot J., Tankov P., “Monte Carlo option pricing for tempered stable (CGMY) processes”, Asia-Pacific Financial Markets, 13:4 (2006), 327–344 | DOI | Zbl

[19] Raible S., Lévy Processes in Finance: Theory, Numerics, and Empirical Facts, PhD thesis, Universität Freiburg, 2000 | Zbl

[20] Rudin W., Real and Complex Analysis, McGraw-Hill, New York, 1966, 412 pp. | MR | Zbl

[21] Sato K.-I., Lévy Processes and Infinitely Divisible Distributions, Cambridge Univ. Press, Cambridge, 1999, 486 pp. | MR

[22] Thomée V., Galerkin Finite Element Methods for Parabolic Problems, Springer, Berlin, 2006, 370 pp. | MR | Zbl

[23] von Petersdorff T., Schwab C., “Wavelet discretizations of parabolic integrodifferential equations”, SIAM J. Numer. Anal., 41:1 (2003), 159–180 | DOI | MR | Zbl

[24] Wloka J., Partial Differential Equations, Cambridge Univ. Press, Cambridge, 1987, 518 pp. | MR | Zbl

[25] Zeidler E., Nonlinear Functional Analysis and its Applications. V. II/A: Linear Monotone Operators, Springer-Verlag, New York, 1990, 467 pp. | MR