On the Convergence of the p-Optimal Martingale Measures to the Minimal Entropy Martingale Measure

References

• El Karoui , N. , and M.C. Quenez . 1995 . Dynamic programming and pricing of contingent claims in an incomplete market . SIAM J. Control Optim. 33 : 29 – 66 .
   Web of Science ®Google Scholar
• Delbaen , F. , and W. Schachermayer . 1996 . The variance-optimal martingale measure for continuous processes . Bernoulli 2 : 81 – 105 .
   Google Scholar
• Schweizer , M. 1996 . Approximation pricing and the variance optimal martingale measure . Ann. Probab. 24 : 206 – 236 . [CROSSREF]
   Web of Science ®Google Scholar
• Frittelli , M. 2000 . The minimal entropy martingale measure and the valuation problem in incomplete markets . Math. Finance 10 : 39 – 52 . [CROSSREF]
   Web of Science ®Google Scholar
• Gourieroux , C. , J.P. Laurent , and H. Pham . Mean-Variance hedging and numeraire . 1998 . Math. Finance 8 : 179 – 200 . [CROSSREF]
   Web of Science ®Google Scholar
• Pham , H. , T. Rheinländer , and M. Schweizer . 1998 . Mean-variance hedging for continuous processes: New proofs and examples . Finance andStoch. 2 : 173 – 198 . [CROSSREF]
   Google Scholar
• Delbaen , F. , P. Grandits , T. Rheinländer , D. Samperi , M. Schweizer , and C. Stricker . 2002 . Exponential hedging and entropic penalties . Math. Finance 12 : 99 – 123 . [CROSSREF]
   Web of Science ®Google Scholar
• Rouge , R. , and N. El Karoui . 2000 . Pricing via utility maximization and entropy . Math. Finance 10 : 259 – 276 . [CROSSREF]
   Web of Science ®Google Scholar
• Grandits , P. , and L. Krawczyk . 1998 . Closeness of some spaces of stochastic integrals . In Séminaire de Probabilités XXXII , eds. J. Azéma , M. Émery , M. Ledoux and M. Yor , Lect. Notes in Math. New York : Springer . 73 – 85 .
   Google Scholar
• Grandits , P. 1999 . The p-optimal martingale measure and its asymptotic relation with the minimal entropy martingale measure . Bernoulli 5 : 225 – 247 .
   Web of Science ®Google Scholar
• Grandits , P. , and T. Rheinländer . 2002 . On the minimal entropy martingale measure . Ann. Probab. 30 : 1003 – 1038 . [CROSSREF]
   Web of Science ®Google Scholar
• Bellini , F. , and M. Frittelli . 2002 . On the existence of minimax martingale measures . Math. Finance 12 : 1 – 21 . [CROSSREF]
   Web of Science ®Google Scholar
• Goll , T. , and L. Rüschendorf . 2001 . Minimax and minimal distance martingale measures and their relationship to portfolio optimization . Finance Stoch. 5 : 557 – 581 . [CROSSREF]
   Google Scholar
• Mania , M. , M. Santacroce , and Tevzadze , R. . 2003 . A Semimartingale BSDE related to the minimal entropy martingale measure . Finance Stoch. 7 : 385 – 402 . [CROSSREF]
   Web of Science ®Google Scholar
• Mania , M. , M. Santacroce , and Tevzadze , R. . 2002 . A Semimartingale backward equation related to the p -optimal martingale measure and the lower price of a contingent claim. In Stoch. Processes and Related Topics , eds. R. Buckdahn , H.-J. Engelbert , and M. Yor , Vol. 12 , 189 – 212 . London : Taylor & Francis .
   Google Scholar
• Hobson , D. 2004 . Stochastic volatility models, correlation and the q-optimal measure . Math. Finance , 14 : 537 – 556 . [CROSSREF]
   Web of Science ®Google Scholar
• Chitashvili , R. 1983 . Martingale ideology in the theory of controlled stochastic processes. In Probability Theory and Mathematical Statistics , eds. K. Ito and J.V. Prokhorov , 73 – 92 , Lect. Notes in Math. Berlin : Springer .
   Google Scholar
• Pardoux , E. , and S. Peng . 1990 . Adapted solution of a backward stochastic differential equation . Systems Control Lett. 14 : 55 – 61 . [CROSSREF]
   Web of Science ®Google Scholar
• El Karoui , N. S. Peng , M. C. Quenez . 1997 . Backward stochastic differential equations in finance . Math. Finance 7 ( N.1 ): 1 – 71 . [CROSSREF]
   Web of Science ®Google Scholar
• Dellacherie , C. , and P.A. Meyer . 1982 . Probabilities and potential. B. Theory of Martingales. Amsterdam : North-Holland Publishing Co.
   Google Scholar
• Jacod , J. 1979 . Calcule Stochastique et Problèmes Des Martingales . Lecture Notes in Math. Berlin : Springer
   Google Scholar
• Liptser , R.Sh. , and A.N. Shiryaev . 1986 . Martingale Theory. Moscow : Nauka .
   Google Scholar
• Doléans-Dade , K. and P.A. Meyer . 1979 . Inégalités de normes avec poids. In Séminaire de Probabilités XIII , eds. C. Dellacherie , P.A. Meyer , and M. Weil , 204 – 215 , Lect. Notes in Math. Berlin : Springer
   Google Scholar
• Kazamaki , N. 1994 . Continuous Exponential Martingales and BMO . Lecture Notes in Math. Berlin : Springer .
   Google Scholar
• Csiszár , I. 1975 . I divergence geometry of probability distributions and minimization problems . Ann. Probab. 3 : 146 – 158 .
   Web of Science ®Google Scholar
• Kabanov , Y. , and C. Stricker . 2001 . On equivalent martingale measures with bounded densities. In Séminaire de Probabilités, XXXV , eds. J. Azéma , M. Émery , M. Ledoux and M. Yor , 139 – 148 , Lecture Notes in Math. Berlin : Springer
   Google Scholar
• Rheinländer , T. 1999 . Optimal Martingale Measures and their Applications in Mathematical Finance . Ph.D thesis ; Tech. Universität Berlin: : Berlin .
   Google Scholar
• Kabanov , Y. , R.Sh. Liptser , and A. N. Shiryaev . 1986 . On the variation distance for probability measures defined on a filtered space . Probab. Th. Rel. Fields 71 : 19 – 35 . [CROSSREF]
   Web of Science ®Google Scholar