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@article{MM_2011_23_5_a6, author = {O. E. Kudryavtsev}, title = {Efficient numerical method for solving a~special class of integro-differential equations connected with {Levy} models}, journal = {Matemati\v{c}eskoe modelirovanie}, pages = {95--104}, publisher = {mathdoc}, volume = {23}, number = {5}, year = {2011}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MM_2011_23_5_a6/} }
TY - JOUR AU - O. E. Kudryavtsev TI - Efficient numerical method for solving a~special class of integro-differential equations connected with Levy models JO - Matematičeskoe modelirovanie PY - 2011 SP - 95 EP - 104 VL - 23 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MM_2011_23_5_a6/ LA - ru ID - MM_2011_23_5_a6 ER -
%0 Journal Article %A O. E. Kudryavtsev %T Efficient numerical method for solving a~special class of integro-differential equations connected with Levy models %J Matematičeskoe modelirovanie %D 2011 %P 95-104 %V 23 %N 5 %I mathdoc %U http://geodesic.mathdoc.fr/item/MM_2011_23_5_a6/ %G ru %F MM_2011_23_5_a6
O. E. Kudryavtsev. Efficient numerical method for solving a~special class of integro-differential equations connected with Levy models. Matematičeskoe modelirovanie, Tome 23 (2011) no. 5, pp. 95-104. http://geodesic.mathdoc.fr/item/MM_2011_23_5_a6/
[1] Uchaikin V. V., Metod drobnykh proizvodnykh, Artishok, Ulyanovsk, 2008, 512 pp.
[2] Bogomolov S. V., “Metod chastits. Neszhimaemaya zhidkost”, Matem. modelirovanie, 15:1 (2003), 46–58 | MR | Zbl
[3] Dubkov A. A., Spanolo B., “Statsionarnye veroyatnostnye kharakteristiki superdiffuzii”, Aktualnye problemy statisticheskoi radiofiziki, 5 (2006), 55–65
[4] Cont R., Tankov P., Financial modelling with jump processes, Chapman and Hall/CRC Press, New York, 2004, 527 pp. | MR
[5] Kudryavtsev O. E., Levendorskii S. Z., “Fast and accurate pricing of barrier options under Levy processes”, Finance Stoch., 13:4 (2009), 531–562 | DOI | MR | Zbl
[6] Kudryavtsev O. E., “Vychislenie tsen barernykh i amerikanskikh optsionov v modelyakh Levi”, Obozrenie prikladnoi i promyshlennoi matematiki, 17:2 (2010), 210–220
[7] Kudryavtsev O. E., “Bystryi i effektivnyi metod otsenivaniya barernykh optsionov v modelyakh Levi s pereklyucheniem rezhimov po parametram protsessa”, Nauchno-tekhnicheskie vedomosti SPbGPU. Seriya “Informatika. Telekommunikatsii. Upravlenie”, 93:1 (2010), 136–141
[8] Kudryavtsev O. E., “Effektivnyi chislennyi metod otsenivaniya amerikanskikh optsionov v modelyakh Levi s pereklyucheniem rezhimov po parametram protsessa”, Vestnik RGUPS, 39:3 (2010), 158–167
[9] Baxendale P., Stochastic differential equations: theory and applications, Interdisciplinary Mathematical Sciences, 2, World Scientific, Hackensack, NJ, 2007, 393 pp. | MR | Zbl
[10] Boyarchenko S. I., Levendorskii S. Z., Non-Gaussian Merton-Black-Scholes theory, World Scientific, River Edge, NJ, 2002, 398 pp. | MR | Zbl
[11] Boyer R. H., “An integro-differential equation for a Markov process”, J. Soc. Industr. and Appl. Math., 7:4 (1959), 473–486 | DOI | MR | Zbl
[12] Bakshia G., Panayotov G., “First-Passage Probability, Jump Models, and Intra-Horizon Risk”, Journal of Financial Economics, 95:1 (2010), 20–40 | DOI
[13] Novikov A., Melchers R. E., Shinjikashvili E., Kordzakhia N., “First passage time of filtered Poisson process with exponential shape function”, Probab. Eng. Mech., 20:1 (2005), 57–65 | DOI
[14] Sato K., Levy processes and infinitely divisible distributions, Cambridge University Press, Cambridge, 1999, 486 pp. | MR | Zbl
[15] Abate J., Whitt W., “A unified framework for numerically inverting Laplace transforms”, INFORMS J. Comput., 18 (2006), 408–421 | DOI | MR
[16] Abate J., Whitt W., “Numerical inversion of Laplace transforms of probability distributions”, ORSA Journal on Computing, 7 (1995), 36–43 | Zbl