Finite utility on financial markets with asymmetric information and structure properties of the price dynamics

Ankirchner, Stefan; Imkeller, Peter

doi:10.1016/j.anihpb.2004.03.008

Ankirchner, Stefan ; Imkeller, Peter

Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 479-503

MR Zbl

DOI : 10.1016/j.anihpb.2004.03.008

@article{AIHPB_2005__41_3_479_0,
     author = {Ankirchner, Stefan and Imkeller, Peter},
     title = {Finite utility on financial markets with asymmetric information and structure properties of the price dynamics},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {479--503},
     year = {2005},
     publisher = {Elsevier},
     volume = {41},
     number = {3},
     doi = {10.1016/j.anihpb.2004.03.008},
     mrnumber = {2139030},
     zbl = {02191864},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpb.2004.03.008/}
}

TY  - JOUR
AU  - Ankirchner, Stefan
AU  - Imkeller, Peter
TI  - Finite utility on financial markets with asymmetric information and structure properties of the price dynamics
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2005
SP  - 479
EP  - 503
VL  - 41
IS  - 3
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpb.2004.03.008/
DO  - 10.1016/j.anihpb.2004.03.008
LA  - en
ID  - AIHPB_2005__41_3_479_0
ER  -

%0 Journal Article
%A Ankirchner, Stefan
%A Imkeller, Peter
%T Finite utility on financial markets with asymmetric information and structure properties of the price dynamics
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2005
%P 479-503
%V 41
%N 3
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpb.2004.03.008/
%R 10.1016/j.anihpb.2004.03.008
%G en
%F AIHPB_2005__41_3_479_0

Ankirchner, Stefan; Imkeller, Peter. Finite utility on financial markets with asymmetric information and structure properties of the price dynamics. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 3, pp. 479-503. doi: 10.1016/j.anihpb.2004.03.008

Bibliographie
Cité par

[1] J. Amendinger, Initial enlargement of filtrations and additional information in financial markets, Thesis, TU Berlin, 1999. | Zbl

[2] J. Amendinger, D. Becherer, M. Schweizer, A monetary value for initial information in portfolio optimization, Finance and Stochastics 7 (1) (2003) 29-46. | Zbl | MR

[3] J. Amendinger, P. Imkeller, M. Schweizer, Additional logarithmic utility of an insider, Stochastic Process. Appl. 75 (1998) 263-286. | Zbl | MR

[4] S. Ankirchner, Information and semimartingales, PhD thesis, HU Berlin, 2005.

[5] F. Baudoin, Conditioned stochastic differential equations: theory, examples, and applications to finance, Stochastic Process. Appl. 100 (2002) 109-145. | Zbl | MR

[6] F. Baudoin, Modeling Anticipations on Financial Markets, Paris-Princeton Lectures on Mathematical Finance 2002, Springer, Berlin, 2003. | Zbl | MR

[7] F. Baudoin, L. Nguyen-Ngoc, The financial value of a weak information on a financial market, Finance and Stochastics 8 (2004) 415-435. | Zbl | MR

[8] F. Biagini, B. Oksendal, A general stochastic calculus approach to insider trading, Preprint, Univ. of Oslo, 2003. | MR

[9] M. Chaleyat-Maurel, T. Jeulin, Grossissement Gaussien de la filtration Brownienne, in: Jeulin T., Yor M. (Eds.), Grossissements de filtrations : exemples et applications, Lecture Notes in Math., vol. 1118, Springer, Berlin, 1985. | Zbl | MR

[10] J.M. Corcuera, P. Imkeller, A. Kohatsu-Higa, D. Nualart, Additional utility of insiders with imperfect dynamical information, Finance and Stochastics 8 (2004) 437-450. | Zbl | MR

[11] F. Delbaen, W. Schachermayer, A general version of the fundamental theorem of asset pricing, Math. Ann. 300 (1994) 463-520. | Zbl | MR

[12] F. Delbaen, W. Schachermayer, The existence of absolutely continuous local martingale measures, Ann. Appl. Probab. 5 (1995) 926-945. | Zbl | MR

[13] F. Delbaen, W. Schachermayer, Arbitrage possibilities in Bessel processes and their relation to local martingales, Probab. Theory Related Fields 102 (1995) 357-366. | Zbl | MR

[14] F. Delbaen, W. Schachermayer, The variance-optimal martingale measure for continuous processes, Bernoulli 2 (1996) 81-105. | Zbl | MR

[15] C. Dellacherie, B. Maisonneuve, P.-A. Meyer, Probabilités et potentiel, Chap. XVII-XXIV, Hermann, Paris, 1992.

[16] A. Grorud, M. Pontier, Insider trading in a continuous time market model, Int. J. Theoret. Appl. Finance 1 (1998) 331-347. | Zbl

[17] P. Imkeller, Random times at which insiders can have free lunches, Stochastics Stochastics Rep. 74 (2002) 465-487. | Zbl | MR

[18] P. Imkeller, Malliavin's calculus in insider models: additional utility and free lunches, Math. Finance 13 (2003) 153-169. | Zbl | MR

[19] P. Imkeller, M. Pontier, F. Weisz, Free lunch and arbitrage possibilities in a financial market model with an insider, Stochastic Process. Appl. 92 (2001) 103-130. | Zbl | MR

[20] J. Jacod, Grossissement initial, hypothèse $(H^{'})$ et théorème de Girsanov, in: Jeulin T., Yor M. (Eds.), Grossissements de filtrations : exemples et applications, Lecture Notes in Math., vol. 1118, Springer, Berlin, 1985. | Zbl

[21] T. Jeulin, Semi-martingales et grossissement de filtration, Lecture Notes in Math., vol. 833, Springer, Berlin, 1980. | Zbl | MR

[22] I. Karatzas, I. Pikovsky, Anticipative portfolio optimization, Adv. Appl. Probab. 28 (1996) 1095-1122. | Zbl | MR

[23] D. Kramkov, W. Schachermayer, The asymptotic elasticity of utility functions and optimal investment in incomplete markets, Ann. Appl. Probab. 9 (1999) 904-950. | Zbl | MR

[24] J.A. Leon, R. Navarro, D. Nualart, An anticipative calculus approach to the utility maximization of an insider, Math. Finance 13 (2003). | Zbl | MR

[25] P.A. Meyer, Sur un théorème de Jacod, Sém. de Probabilités XII, Lecture Notes in Math., vol. 649, Springer, Berlin, 1978. | Zbl | Numdam

[26] D. Nualart, The Malliavin Calculus and Related Topics, Springer, Berlin, 1995. | Zbl | MR

[27] P. Protter, Stochastic Integration and Differential Equations, Springer, Berlin, 2004. | Zbl | MR

[28] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1999. | Zbl | MR

[29] F. Russo, P. Vallois, Forward, backward and symmetric stochastic integration, Probab. Theory Related Fields 97 (1993) 403-421. | Zbl | MR

[30] M. Schweizer, On the minimal martingale measure and the Föllmer-Schweizer decomposition, Stochastic Anal. Appl. 13 (1995) 573-599. | Zbl | MR

[31] S.-Q. Song, Grossissements de filtrations et problemes connexes, Thèse de doctorat, Univ. Pierre et Marie Curie Paris 6, 1987.

[32] C.T. Wu, Construction of Brownian motions in enlarged filtrations and their role in mathematical models of insider trading, Dissertation, HU Berlin, 1999. | Zbl

[33] M. Yor, Grossissement de filtrations et absolue continuité de noyaux, in: Jeulin T., Yor M. (Eds.), Grossissements de filtrations : exemples et applications, Lecture Notes in Math., vol. 1118, Springer, Berlin, 1985. | Zbl | MR

[34] M. Yor, Entropie d'une partition, et grossissement initial d'une filtration, in: Jeulin T., Yor M. (Eds.), Grossissements de filtrations : exemples et applications, Lecture Notes in Math., vol. 1118, Springer, Berlin, 1985. | Zbl | MR

[35] M. Yor, Inégalités de martingales continues arrêtées à un temps quelconque, I : théorèmes généraux, in: Jeulin T., Yor M. (Eds.), Grossissements de filtrations : exemples et applications, Lecture Notes in Math., vol. 1118, Springer, Berlin, 1985. | Zbl

[36] M. Yor, Inégalités de martingales continues arrêtées à un temps quelconque, II : le rôle de certains espaces BMO, in: Jeulin T., Yor M. (Eds.), Grossissements de filtrations : exemples et applications, Lecture Notes in Math., vol. 1118, Springer, Berlin, 1985. | Zbl | MR

Cité par Sources :