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Original Articles

The Minimal Entropy and the Convergence of the p-Optimal Martingale Measures in a General Jump Model

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Pages 941-977 | Received 16 Apr 2007, Accepted 29 Jan 2008, Published online: 28 Aug 2008

REFERENCES

  • Arai , T. 2004 . Minimal martingale measures for jump diffusion processes . Journal of Applied Probability 41 : 263 – 270 .
  • Arai , T. 2005 . An extension of mean-variance hedging to the discontinuous case . Finance Stochastics 9 : 129 – 139 .
  • Bobrovnytska , O. , and Schweizer , M. 2004 . Mean-variance headging and stochastic control: Beyond the Brownian setting . IEEE Transactions on Automatic Control 49 : 396 – 408 .
  • Bonami , A. , and Lepingle , D. 1979 . Fonction Maximale et Variation Quadratique des Martingales en Présence d'un Poids, Séminaire de Probabilités XIII, , Lecture Notes in Mathematics 721, Springer , 294 – 306 .
  • Chan , T. 1999 . Pricing contingent claims on stocks driven by Lévy processes . Annals of Applied Probability 9 : 504C528 .
  • Cont , R. , and Tankov , P. 2004 . Financial Modeling with Jump Processes . Chapman & Hall/CRC , Boca Raton, FL .
  • Cont , R. , Tankov , P. , and Voltchkova , E. 2004 . Option pricing models with jumps: integro-differential equations and inverse problems . In European Congress on Computational Methods in Applied Sciences and Engineering . P. Neittaanmäki , T. Rossi , S. Korotov , E. Oñate , J. Périaux , D. Knörzer , (eds). Jyväskylä, 24C28 July .
  • Delbaen , F. , and Schachermayer , W. 1996 . The variance-optimal martingale measure for continuous processes . BERNOULLI 2 : 81 – 105 .
  • Doléans-Dade , C. , and Meyer , P.A. 1979 . Inégalités de Normes avec Poids, Séminaire de Probabilités XIII, , Lecture Notes in Mathematics 721, Springer , 313 – 331 .
  • Emmer , S. , and Klüppelberg , C. 2004. Optimal portfolios when stock prices follow an exponential Lévy process. Finance Stochastics 8:17C44.
  • Frittelli , M. 2000 . The minimal entropy martingale measure and the valuation problem in incomplete markets . Mathematical Finance 10 ( 1 ): 39 – 52 .
  • Fujiwara , T. , and Miyahara , Y. 2003 . The minimal entropy martingale measures for geometric Lévy processes . Finance Stochastics 7 : 509 – 531 .
  • Gourieroux , C. , Laurent , J.P. , and Pham , H. 1998 . Mean-variance hedging and numéraire . Mathematical Finance 8 ( 3 ): 179 – 200 .
  • Grandits , P. , and Rheinländer , T. 2002 . On the minimal entropy martingale measure . Annals of Probability 30 ( 3 ): 1003 – 1038 .
  • Jacod , J. , and Shiryaev , A.N. 1987 . Limit Theorems for Stochastic Processes . Springer , Berlin .
  • Jacod , J. 1979 . Calcul Stochastique et Problèmes de Martingales . Lecture Notes in Mathematics , Springer , Berlin , 714 .
  • Jeanblanc , M. , Kloeppel , S. , and Miyahara , Y. 2006 . Minimal f q -martingale measures for exponential Lévy processes . Preprint Université d'Evry Val d'Essonne and Europlace de France , Vienna University of Technology, and Nagoya City University .
  • El Karoui , N. , and Quenez , M.C. 1995 . Dynamic programming and pricing of contingent claims in an incomplete market . SIAM Journal of Control Optimization 33 : 29 – 66 .
  • Kohlmann , M. , and Niethammer , C.R. 2007 . On convergence to the exponential utility problem . Stochastic Processes and Applications 117 ( 12 ): 1813 – 1834 .
  • Kohlmann , M. , Xiong , D. , and Ye , Z. 2007 . Change of filtrations and mean-variance hedging . Stochastics, IJPSP 79 ( 6 ): 539 – 562 .
  • Kohlmann , M. , and Xiong , D. 2007 . The p-optimal martingale measure when there exist inaccessible jumps . International Journal of Pure and Applied Mathematics 37 ( 3 ): 321 – 348 .
  • Kunita , H. 2004 . Representation of martingales with jumps and applications to mathematical finance . Stochastic Analysis and Related Topics 41 : 209 – 232 .
  • Laurent , J.P. , and Pham , H. 1999 . Dynamic programming and mean-variance headging . Finance and Stochastics 3 : 83 – 110 .
  • Mania , M. , Santacroce , M. , and Tevzadze , R. 2002 . A semimartingale backward equation related to the p-optimal martingale measure and the lower price of a contingent claim . In Stochastic Processes and Related Topics, Stochastics Monograph, Vol. 12 , Taylor Francis, London , pp. 182 – 212 .
  • Mania , M. , Santacroce , M. , and Tevzadze , R. 2003 . A semimartingale BSDE related to the minimal entropy martingale measure . Finance Stochastics 7 : 385 – 402 .
  • Niethammer , C.R. 2008 . On convergence to the exponential utlity problem with jumps . Stochastic Analysis and Applications 26 ( 1 ): 169 – 196 .
  • Runggaldier , W.J. 2002 . Jump-diffusion models . Preprint , Universita di Padova , Italy .
  • Rheinländer , Th . 1999 . Optimal Martingale Measures and Their Applications in Mathematical Finance . Berlin, Ph.D. Thesis, Technical Universität Berlin .
  • Santacroce , M. 2005. On the convergence of the p-optimal martingale measures to the minimal entropy martingale measure. Stochastic Analysis and Applications 23:31–54.
  • Schweizer , M. 1996 . Approximation pricing and the variance-optimal martingale measure . Annals of Probability 24 : 206 – 236 .

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