Robust utility maximization in terms of supermartingale measures
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2022), pp. 19-25 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a dual description of the optimal value of robust utility in the abstract model of the financial market $(\Omega,\mathscr{F},\mathrm{P},\mathscr{A}(x))$, where $\mathscr{A}(x)=x\mathscr{A}$, $x\geq 0$, is the set of the investor's terminal capitals corresponding to strategies with the initial capital $x$. The main result of the paper addresses the question of the transition in the definition of the dual problem from the polar of the set $\mathscr{A}$ to a narrower set of limit values of supermartingale densities.
@article{VMUMM_2022_1_a2,
     author = {A. A. Farvazova},
     title = {Robust utility maximization in terms of supermartingale measures},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {19--25},
     year = {2022},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2022_1_a2/}
}
TY  - JOUR
AU  - A. A. Farvazova
TI  - Robust utility maximization in terms of supermartingale measures
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2022
SP  - 19
EP  - 25
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2022_1_a2/
LA  - ru
ID  - VMUMM_2022_1_a2
ER  - 
%0 Journal Article
%A A. A. Farvazova
%T Robust utility maximization in terms of supermartingale measures
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2022
%P 19-25
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2022_1_a2/
%G ru
%F VMUMM_2022_1_a2
A. A. Farvazova. Robust utility maximization in terms of supermartingale measures. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2022), pp. 19-25. http://geodesic.mathdoc.fr/item/VMUMM_2022_1_a2/

[1] Felmer G., Shid A., Vvedenie v stokhasticheskie finansy. Diskretnoe vremya, MTsNMO, M., 2008

[2] Guschin A. A., “O rasshirenii ponyatiya f-divergentsii”, Teor. veroyatn. i ee primen., 52:3 (2007), 468–489 | MR

[3] Guschin A. A., “Dvoistvennaya kharakterizatsiya tseny v zadache maksimizatsii robastnoi poleznosti”, Teor. veroyatn. i ee primen., 55:4 (2010), 680–704

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

[5] Brannath W., Schachermayer W., “A bipolar theorem for $L^{0}_{+}(\Omega,\mathcal{F},\mathbb{P})$”, Seminaire de Probabilites XXXIII, Lect. Notes Math., 1709, Springer, Berlin, 1999, 349–354 | DOI | MR | Zbl

[6] Follmer H., Kramkov D., “Optional decompositions under constraints”, Probab. Theory and Related Fields, 109:1 (1997), 1–25 | DOI | MR | Zbl

[7] Rokhlin D. B., “O suschestvovanii ekvivalentnoi supermartingalnoi plotnosti dlya razvetvlenno-vypuklogo semeistva sluchainykh protsessov”, Matem. zametki, 87:4 (2010), 594–603 | Zbl

[8] Zitkovic G. A., “A filtered version of the bipolar theorem of Brannath and Schachermayer”, J. Theor. Probab., 15:1 (2002), 41–61 | DOI | MR | Zbl

[9] Yan J. A., “Caracterisation d'une classe d'ensembles convexes de $L^{1}$ ou $H^{1}$”, Seminaire de Probabilites XIV, Lect. Notes Math., 784, Springer, Berlin, 1980, 220–222 | DOI | MR