Logarithmic utility maximization in an exponential Lévy model
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2014), pp. 16-24 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problems of logarithmic utility maximization and finding the numéraire portfolio in an exponential Lévy model are studied in the paper in terms of Lévy–Khinchin triplet.
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M. Yu. Ivanov. Logarithmic utility maximization in an exponential Lévy model. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2014), pp. 16-24. http://geodesic.mathdoc.fr/item/VMUMM_2014_6_a2/

[1] Karatzas I., Lehoczky J.P., Shreve S.E., “Optimal portfolio and consumption decisions for a “small investor” on a finite horizon”, SIAM J. Control Optim., 25 (1987), 1557–1586 | DOI | MR | Zbl

[2] Kramkov D., Schachermayer W., “The condition on the asymptotic elasticity of utility functions and optimal investment in incomplete markets”, Ann. Appl. Probab., 9:3 (1999), 904–950 | DOI | MR | Zbl

[3] Becherer D., “The numéraire portfolio for unbounded semimartingales”, Finance Stochast., 5 (2001), 327–341 | DOI | MR | Zbl

[4] Essche F., Schweizer M., “Minimal entropy preserves the Levy property: how and why”, Stochast. Proc. Appl., 115:2 (2005), 299–327 | DOI | MR

[5] Jeanblanc M., Klöppel S., Miyahara Y., “Minimal $f^q$-martingale measures for exponential Lévy processes”, Ann. Appl. Probab., 17 (2007), 1615–1638 | DOI | MR | Zbl

[6] Hurd T.R., “A note on log-optimal portfolios in exponential Lévy markets”, Statistics and Decisions, 22 (2004), 225–236 | DOI | MR

[7] Delbaen F., Schachermayer W., “The fundamental theorem of asset pricing for unbounded stochastic processes”, Math. Ann., 312:2 (1998), 215–260 | DOI | MR

[8] Kallsen J., “Optimal portfolios for exponential Lévy processes”, Mathematical Methods of Operations Research, 51 (2000), 357–374 | DOI | MR

[9] Goll T., Kallsen J., “A complete explicit solution to the log-optimal portfolio problem”, Ann. Appl. Probab., 13 (2003), 774–799 | DOI | MR | Zbl

[10] Karatzas I., Kardaras C., “The numéraire portfolio in semimartingale financial models”, Finance Stochast., 11 (2007), 447–493 | DOI | MR | Zbl

[11] Takaoka K., On the condition of no unbounded profit with bounded risk, Working Paper No 131, Graduate School of Commerce and Management. Hitotsubashi University, 2010 http://hdl.handle.net/10086/18812

[12] Kardaras C., “No-free-lunch equivalences for exponential Lévy models under convex constraints on investment”, Math. Finance, 19 (2009), 161–187 | DOI | MR | Zbl

[13] Eberlein E., Jacod J., “On the range of options prices”, Finance Stochast., 1 (1997), 131–140 | DOI | Zbl

[14] Jacubénas P., “On option pricing in certain incomplete markets”, Proc. Steklov Inst. Math., 237 (2002), 114–133

[15] Cherny A. S., Shiryaev A.N., “Change of time and measure for Lévy processes”, Lecture for the Summer School “From Lévy processes to semimartingales: Recent theoretical developments and applications in finance” (Aarhus, 2002)

[16] Selivanov A.V., “O martingalnykh merakh v eksponentsialnykh modelyakh Levi”, Teoriya veroyatnostei i ee primeneniya, 49:2 (2004), 317–334 | DOI | Zbl

[17] Sato K.-I., Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, 1999 | MR

[18] Jacod J., Shiryaev A.N., Limit Theorems for Stochastic Processes, 2nd ed., Springer, N.Y., 2003 | MR | Zbl

[19] Jacod J., Calcul stochastique et problèmes de martingales, Springer, Berlin–Heidelberg–N.Y., 1979 | MR | Zbl