Geodesic
When a stochastic exponential is a true martingale. Extension of the Beneš method
Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 1, pp. 53-80 Cet article a éte moissonné depuis la source Math-Net.Ru

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Keywords: exponential martingale; diffusion process with jumps; Girsanov theorem; Beneš method. 
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F. Klebaner; R. Liptser. When a stochastic exponential is a true martingale. Extension of the Beneš method. Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 1, pp. 53-80. http://geodesic.mathdoc.fr/item/TVP_2013_58_1_a4/

[1] Andersen L. B., Piterbarg V. V., “Moment explosions in stochastic volatility models”, Finance Stoch., 11 (2007), 29–50 | DOI | MR | Zbl

[2] Baudoin F., Nualart D., “Equivalence of Volterra processes”, Stochastic Process. Appl., 107 (2003), 327–350 | DOI | MR

[3] Benes V. E., “Existence of optimal stochastic control laws”, SIAM J. Control, 9 (1971), 446–475 | DOI | MR

[4] Cheridito P., “Mixed fractional Brownian motion”, Bernoulli, 7 (2001), 913–934 | DOI | MR | Zbl

[5] Cheridito P., Filipović D., Yor M., “Equivalent and absolutely continuous measure changes for jump-diffusion processes”, Ann. Appl. Probab., 15:3 (2005), 1713–1732 | DOI | MR | Zbl

[6] Cox J. C., “The constant elasticity of variance option. Pricing model”, J. Portfolio Management, 23:2 (1997), 15–17

[7] Dawson D., “Equivalence of Markov processes”, Trans. Amer. Math. Soc., 131 (1968), 1–31 | DOI | MR | Zbl

[8] Delbaen F., Shirakawa H., “A note on option pricing for constant elasticity of variance model”, Asia-Pac. Financ. Mark., 9:2 (2002), 85–99 | DOI | Zbl

[9] Doléans-Dade C., “Quelques applications de la formule de changement de variables pour les semi-martingales”, Z. Wahrscheinlichkeitstheor. verw. Geb., 16 (1970), 181–194 | DOI | MR | Zbl

[10] Girsanov I. V., “O preobrazovanii nekotorogo klassa sluchainykh protsessov s pomoschyu absolyutno nepreryvnoi zameny mery”, Teoriya veroyatn. i ee primen., 5:2 (1960), 285–301

[11] Hitsuda M., “Representation of Gaussian processes equivalent to Wiener process”, Osaka J. Math., 5 (1968), 299–312 | MR | Zbl

[12] Itô K., Watanabe S., “Transformation of Markov processes by multiplicative functionals”, Ann. Inst. Fourier (Grenoble), 15 (1965), 13–30 | DOI | MR | Zbl

[13] Zhakod Zh., Shiryaev A. N., Predelnye teoremy dlya sluchainykh protsessov, v. 1, Nauka, M., 1994, 542 pp.; т. 2, 366 с.

[14] Kabanov Yu. M., Liptser R. Sh., Shiryaev A. N., “Absolyutnaya nepreryvnost i singulyarnost lokalno absolyutno nepreryvnykh veroyatnostnykh raspredelenii. I; II”, Matem. sb., 107(149):3(11) (1978), 364–415 ; 108(150):1 (1979), 32–61 | MR | Zbl | MR | Zbl

[15] Kadota T., Shepp L., “Conditions for absolute continuity between a certain pair of probability measures”, Z. Wahrscheinlichkeitstheor. verw. Geb., 16 (1970), 250–260 | DOI | MR | Zbl

[16] Kallsen J., Shiryaev A. N., “The cumulant process and Esscher’s change of measure”, Finance Stoch., 6 (2002), 397–428 | DOI | MR | Zbl

[17] Karatzas I., Shreve S. E., Brownian Motion and Stochastic Calculus, Graduate Texts in Math., 113, Springer-Verlag, New York–Berlin–Heidelberg, 1991, 470 pp. | MR | Zbl

[18] Kazamaki N., “On a problem of Girsanov”, Tôhoku Math. J., 29 (1970), 597–600 | DOI | MR

[19] Kazamaki N., Sekiguchi T., “On the transformation of some classes of martingales by a change of law”, Tôhoku Math. J., 31 (1979), 261–279 | DOI | MR | Zbl

[20] Krylov N. V., A simple proof of a result of A. Novikov, 2009, arXiv: 0207013v2 [math.PR]

[21] Kunita H., “Absolute continuity of Markov processes and generators”, Nagoya Math. J., 36 (1969), 1–26 | MR | Zbl

[22] Kunita H., “Absolute continuity of Markov processes”, Lecture Notes in Math., 511, 1976, 44–77 | DOI | MR | Zbl

[23] Lépingle D., Mémin J., “Sur l’intégrabilité uniforme des martingales exponentielles”, Z. Wahrscheinlichkeitstheor. verw. Geb., 42 (1978), 175–203 | DOI | MR | Zbl

[24] Liptser R. Sh., Shiryaev A. N., “Ob absolyutnoi nepreryvnosti mer, sootvetstvuyuschikh protsessam diffuzionnogo tipa, otnositelno vinerovskoi”, Izv. AN SSSR, 36:4 (1972), 847–889 | MR

[25] Liptser R. Sh., Shiryaev A. N., Teoriya martingalov, Nauka, M., 1986, 512 pp. | MR | Zbl

[26] Liptser R. S., Shiryaev A. N., Statistics of Random Processes, v. I, Appl. Math., 5, General Theory, Springer, Berlin, 2001, 427 pp. | MR | Zbl

[27] Liptser R. S., Shiryaev A. N., Statistics of Random Processes, v. II, Appl. Math., 6, Applications, Springer, Berlin, 2001, 402 pp. | MR | Zbl

[28] Liptser R., Beneŝ condition for discontinuous exponential martingale, arXiv: 0911.0641v3 [math.PR] | MR

[29] Mijatović A., Urusov M., “On the martingale property of certain local martingales: criteria and applications”, Probab. Theory Related Fields, 152:1–2 (2012), 1–30, arXiv: 0905.3701v1 [math.PR] | DOI | MR | Zbl

[30] Novikov A. A., “Ob usloviyakh ravnomernoi integriruemosti nepreryvnykh neotritsatelnykh martingalov”, Teoriya veroyatn. i ee primen., 24:4 (1979), 821–825 | MR | Zbl

[31] Palmowski Z., Rolski T., “A technique for exponential change of measure for Markov processes”, Bernoulli, 8 (2002), 767–785 | MR | Zbl

[32] Revuz D., Yor M., Continuous Martingales and Brownian Moton, Grundlehren Math. Wiss., 293, Springer-Verlag, Berlin, 1991, 533 pp. | DOI | MR | Zbl

[33] Rydberg T., “A note on the existence of equivalent martingale measures in a Markovian setting”, Finance Stoch., 1 (1997), 251–257 | DOI | Zbl

[34] Picard J., “Representation formulae for the fractional Brownian motion”, Lecture Notes in Math., 2006, 2011, 3–70, arXiv: 0912.3168v2 [math.PR] | DOI | MR | Zbl

[35] Shiryaev A. N., Osnovy stokhasticheskoi finansovoi matematiki, v. 1, Fakty. Modeli, Fazis, M., 2004; т. 2, Теория, 1017 с.

[36] Sin C. A., “Complications with stochastic volatility models”, Adv. Appl. Probab., 30:1 (1998), 256–268 | DOI | MR | Zbl

[37] Wong B., Heyde C. C., “On the martingale property of stochastic exponentials”, J. Appl. Probab., 41 (2004), 654–664 | DOI | MR | Zbl