Backward stochastic differential equations with enlarged filtration: Option hedging of an insider trader in a financial market with jumps

Stochastic Processes and their Applications

Volumn 115, Issue 11, 2005, Pages 1745-1763

  Eyraud Loisel, Anne ^a  

^a UNIVERSITÉ LYON 1   (France)

Author keywords

Asymmetric information; BSDE; Enlargement of filtration; Insider trading; Martingale representation; Option hedging

Indexed keywords

BROWNIAN MOVEMENT; DIFFERENTIAL EQUATIONS; FILTRATION; INVESTMENTS; MARKETING; MATHEMATICAL MODELS; OPTIMIZATION; STRATEGIC PLANNING;

ASYMMETRIC INFORMATION; BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS (BSDE); ENLARGEMENT OF FILTRATION; INSIDER TRADING; MARTINGALE REPRESENTATION; OPTION HEDGING;

RANDOM PROCESSES;

EID: 25644432046     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2005.05.006     Document Type: Article

References (19)

1. J. Amendinger, Initial enlargement of filtrations and additional information of financial markets, Doctoral Thesis, T-U, Berlin, 1999.
2. J. Amendinger, Martingale representation theorems for initially enlarged filtrations, Stochastic Process. Appl. 89 (2000) 101-116.
3. G. Barles, R. Buckdahn, E. Pardoux, BSDE's and integral-partial differential equations, Stochastics and Stochastic Reports, vol. 60, 1997, pp. 57-83.
4. P. Brémaud, and M. Yor Changes of filtrations and of probability measures Z. Wahrsch. Verw. Gebiete 45 4 1978 269 295
5. M. Chaleyat-Maurel, T. Jeulin, Grossissement gaussien de la filtration brownienne, Séminaire de Calcul stochastique, 1982-83, Paris, Lecture Notes in Mathematics, vol. 1118, Springer, Berlin, 1985, pp. 59-109.
6. N. El Karoui, S. Peng, and M.C. Quenez Backward stochastic differential equations in finance Math. Finance 7 1 1997 1 71
7. A. Grorud Asymmetric information in a financial market with jumps Internat. J. Theoret. Appl. Finance 3 4 2000 641 659
8. A. Grorud, M. Pontier, Comment détecter le délit d'initié?, C.R. Acad. Sci. Paris, t.324, Serie I, (1997) 1137-1142, Probabilités.
9. A. Grorud, and M. Pontier Insider trading in a continuous time market model IJTAF 1 3 1998 331 347
10. A. Grorud, M. Pontier, Probabilités neutres au risque et asymétrie d'information, C.R. Acad. Sci. Paris, t.329, Série I, (1999) 1009-1014, Probabilités.
11. A. Grorud, and M. Pontier Asymmetrical information and incomplete markets Internat. J. Theoret. Appl. Finance 4 2 2001 285 302
12. J. Jacod, Grossissement initial, Hypothèse H' et Théorème de Girsanov, Séminaire de calcul stochastique 1982-83, Paris, Lecture Notes in Mathematics, vol. 1118, Springer, Berlin, 1985, 15-35.
13. J. Jacod, and A.N. Shiryaev Limit Theorems for Stochastic Processes second ed. 2003 Springer Berlin
14. I. Karatzas, S.E. Shreve, Brownian Motion and Stochastic Calculus, second ed., Graduate Texts in Mathematics, vol. 113, Springer, Berlin, 1991.
15. P.A. Meyer, Sur un théorème de J. Jacod, Sémin. Probab. XII, Univ. Strasbourg 1976/77, Lecture Notes in Mathematics, vol. 649, pp. 57-60.
16. E. Pardoux BSDE's, weak convergence and homogeneisation of semilinear PDE's 1998 SMS Montreal
17. E. Pardoux, S. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14 (1990) 55-61.
18. S. Tang, and X. Li Necessary conditions for optimal control of stochastic systems with random jumps SIAM J. Control Optim. 32 5 1994
19. I. Karatzas, S. Shreve, Methods of Mathematical Finance, Applications of Mathematics (New York), vol. 39, Springer-Verlag, New York, 1998.