@book {Rock, AUTHOR = {Rockafellar, R. Tyrrell}, TITLE = {Convex analysis}, SERIES = {Princeton Mathematical Series, No. 28}, PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, N.J.}, YEAR = {1970}, PAGES = {xviii+451}, } @article {MR2194899, AUTHOR = {Platen, Eckhard}, TITLE = {A benchmark approach to finance}, JOURNAL = {Math. Finance}, FJOURNAL = {Mathematical Finance. An International Journal of Mathematics, Statistics and Financial Economics}, VOLUME = {16}, YEAR = {2006}, NUMBER = {1}, PAGES = {131--151}, } @book {MR2267213, AUTHOR = {Platen, Eckhard and Heath, David}, TITLE = {A benchmark approach to quantitative finance}, SERIES = {Springer Finance}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {2006}, PAGES = {xvi+700}, } %%%%%%%%%%%%%%%%%%%%%%%%%%%---Karatzas---%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @article {MR2335830, AUTHOR = {I. Karatzas and K. Constantinos}, TITLE = {The num\'eraire portfolio in semimartingale financial models}, JOURNAL = {Finance Stoch.}, FJOURNAL = {Finance and Stochastics}, VOLUME = {11}, YEAR = {2007}, NUMBER = {4}, PAGES = {447--493}, ISSN = {0949-2984}, } @book{KaratzasShreve:01, author = {I. Karatzas and S. E. Shreve }, howpublished = {Hardcover}, month = {September}, publisher = {Springer}, title = {Methods of Mathematical Finance}, year = {2001} } @article {Karatzas03, AUTHOR = {J. Cvitani{\'c} and I. Karatzas}, TITLE = {Convex duality in constrained portfolio optimization}, JOURNAL = {Ann. Appl. Probab.}, FJOURNAL = {The Annals of Applied Probability}, VOLUME = {2}, YEAR = {1992}, NUMBER = {4}, PAGES = {767--818}, } @article {Karatzas04, AUTHOR = {I. Karatzas, John P. Lehoczky, and Steven E. Shreve and Xu, Gan-Lin}, TITLE = {Martingale and duality methods for utility maximization in an incomplete market}, JOURNAL = {SIAM J. Control Optim.}, FJOURNAL = {SIAM Journal on Control and Optimization}, VOLUME = {29}, YEAR = {1991}, NUMBER = {3}, PAGES = {702--730}, } @article{Karatzas09, author = {I. Karatzas and Wang Hui}, title = {Utility Maximization with Discretionary Stopping}, journal = {SIAM J. Control Optim.}, volume = {39}, number = {1}, year = {2000}, issn = {0363-0129}, pages = {306--329}, doi = {http://dx.doi.org/10.1137/S0363012998346323}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia, PA, USA}, } %%%%%%%%%%%%%%%%%%%%%%%%%%%---Kunita---%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @book{Kunita:01, author = {H. Kunita }, publisher = {Cambridges studies advanced mathematics}, title = {Stochastic Flows and Stochastic Differential Equations}, pages = {364}, year = {1997} } %%%%%%%%%%%%%%%%%%%%%%%%%%%---Kramkov---%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @ARTICLE{KramkovAsy, author = {D. Kramkov and W. Schachermayer}, title = {The asymptotic elasticity of utility functions and optimal investment in incomplete markets}, journal = {Annals of Applied Probability}, year = {1999}, volume = {9}, pages = {904--950} } @article {DelSCH01, AUTHOR = {F. Delbaen and W. Schachermayer}, TITLE = {A general version of the fundamental theorem of asset pricing}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {300}, YEAR = {1994}, NUMBER = {3}, PAGES = {463--520}, ISSN = {0025-5831}, CODEN = {MAANA}, MRCLASS = {90A09 (60G44)}, MRNUMBER = {MR1304434 (95m:90022b)}, MRREVIEWER = {P. E. Kopp}, DOI = {10.1007/BF01450498}, URL = {http://dx.doi.org/10.1007/BF01450498}, } @article {DelSCH02, AUTHOR = {Delbaen, F. and Schachermayer, W.}, TITLE = {The fundamental theorem of asset pricing for unbounded stochastic processes}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {312}, YEAR = {1998}, NUMBER = {2}, PAGES = {215--250}, ISSN = {0025-5831}, CODEN = {MAANA}, MRCLASS = {60G44 (60G05 90A09)}, MRNUMBER = {MR1671792 (99k:60117)}, MRREVIEWER = {Martin Schweizer}, DOI = {10.1007/s002080050220}, URL = {http://dx.doi.org/10.1007/s002080050220}, } @article {MR2014244, AUTHOR = {Schachermayer, W.}, TITLE = {A super-martingale property of the optimal portfolio process}, JOURNAL = {Finance Stoch.}, FJOURNAL = {Finance and Stochastics}, VOLUME = {7}, YEAR = {2003}, NUMBER = {4}, PAGES = {433--456}, ISSN = {0949-2984}, MRCLASS = {91B28 (90C26 91B16)}, MRNUMBER = {2014244 (2005b:91132)}, MRREVIEWER = {Goran Peskir}, DOI = {10.1007/s007800200096}, URL = {http://dx.doi.org/10.1007/s007800200096}, } %%%%%%%%%%%%%%%%%%%%%%%%%%%---Roger's---%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @Article{Mike, author = {F.P.Y.S. Berrier, L.C.G. Rogers, M.R. Tehranchi}, title = {A characterization of forward utility functions}, journal={Preprint}, year = {2009} } %%%%%%%%%%%%%%%%%%%%%%%%%%%---Zariphopoulou---%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @article{zar-03, author = {M. Musiela and T. Zariphopoulou }, title = {Backward and forward utilities and the associated pricing systems: The case study of the binomial model}, journal={Preprint}, year = 2003, } @article{zar-07, author = {M. Musiela and T. Zariphopoulou }, title = {Stochastic partial differential equations in portfolio choice }, journal={Preliminary report}, year = 2007, } @incollection {zar-07a, AUTHOR = {M. Musiela and T. Zariphopoulou}, TITLE = {Investment and valuation under backward and forward dynamic exponential utilities in a stochastic factor model}, BOOKTITLE = {Advances in mathematical finance}, SERIES = {Appl. Numer. Harmon. Anal.}, PAGES = {303--334}, PUBLISHER = {Birkh\"auser Boston}, ADDRESS = {Boston, MA}, YEAR = {2007}. } @article{zar-08, author = {Musiela, M. and Zariphopoulou, T. }, citeulike-article-id = {4279134}, doi = {10.1080/14697680802624997}, issn = {1469-7688}, journal = {Quantitative Finance}, number = {2}, pages = {161--170}, publisher = {Routledge, part of the Taylor \& Francis Group}, title = {Portfolio choice under dynamic investment performance criteria}, YEAR = {2008}, volume = {9} } @article{zar-08a, author = {Musiela, M. and Zariphopoulou, T. }, journal = {Preprint}, keywords = {file-import-09-03-20}, title = {Portfolio choice under space-time monotone performance criteria}, year = {November-2008} } %%%%%%%%%%%%%%%%%%%%%%%%%%%---Zitkovic---%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @article{zitkovic, author = {G. Zitkovic}, title = {A dual characterization of self-generation and log-affine forward performances}, journal = {Preprint}, url = {http://www.citebase.org/abstract?id=oai:arXiv.org:0809.0739}, year = {2008} } %%%%%%%%%%%%%%%%%%%%%%%%%%%---Schachermayer---%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @INPROCEEDINGS{Schachermayer01optimalinvestment, author = {W. Schachermayer}, title = {Optimal investment in incomplete financial markets}, booktitle = {Mathematical Finance: Bachelier Congress 2000}, year = {2001}, pages = {427--462}, publisher = {Springer} } @article {MR1381678, AUTHOR = {F. Delbaen and W. Schachermayer}, TITLE = {The no-arbitrage property under a change of num\'eraire}, JOURNAL = {Stochastics Stochastics Rep.}, FJOURNAL = {Stochastics and Stochastics Reports}, VOLUME = {53}, YEAR = {1995}, NUMBER = {3-4}, PAGES = {213--226}, } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @article {Kardaras, AUTHOR = {C. Kardaras}, TITLE = {Generalized supermartingale deflators under limited information}, JOURNAL = {Mathematical Finance}, VOLUME = {23}, YEAR = {2013}, NUMBER = {1}, PAGES = {186?197}, } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @article{Ing, author = {Ingram,, John M. and Marsh,, M. M.}, title = {Projections onto convex cones in Hilbert space}, journal = {J. Approx. Theory}, volume = {64}, number = {3}, year = {1991}, issn = {0021-9045}, pages = {343--350}, doi = {http://dx.doi.org/10.1016/0021-9045(91)90067-K}, publisher = {Academic Press, Inc.}, address = {Orlando, FL, USA}, } @article {Hobson, AUTHOR = {V. Henderson D. and Hobson}, TITLE = {Horizon-unbiased utility functions}, JOURNAL = {Stochastic Process. Appl.}, FJOURNAL = {Stochastic Processes and their Applications}, VOLUME = {117}, YEAR = {2007}, NUMBER = {11}, PAGES = {1621--1641}, } @article{Zongxia, Author ={L. Zongxia }, title ={ Stochastic Differential Equations Driven by Spatial Parameters Semimartingale with Non-Lipschitz Local Characteristic}, journal = {Potential Analysis}, volume= {26}, Issue ={4}, Page ={307-322}, year={ 2007}, DOI ={ 10.1007/s11118-007-9038-4}, doi = {http://www.springerlink.com/content/90217w1627247278}, } @book {Pham, AUTHOR = {P. Huy{\^e}n}, TITLE = {Optimisation et contr\^ole stochastique appliqu\'es \`a la finance}, SERIES = {Math\'ematiques \& Applications (Berlin) [Mathematics \& Applications]}, VOLUME = {61}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {2007}, PAGES = {xvi+186}, } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @incollection {MR1119828, AUTHOR = {R. J.Elliott and H. F{\"o}llmer}, TITLE = {Orthogonal martingale representation}, BOOKTITLE = {Stochastic analysis}, PAGES = {139--152}, PUBLISHER = {Academic Press}, ADDRESS = {Boston, MA}, YEAR = {1991}, } @article{crisli92, archivePrefix = {arXiv}, author = {Crandall, M. G. and Ishii, H. and Lions, P. L.}, citeulike-article-id = {3934987}, eprint = {math/9207212}, journal = {ArXiv Mathematics e-prints}, keywords = {viscosity-solution}, month = {June}, posted-at = {2009-01-24 00:46:10}, priority = {2}, title = {User's guide to viscosity solutions of second order partial differential equations}, url = {http://arxiv.org/abs/math/9207212}, year = {1992} } @article {MRADNEK01, AUTHOR = {N. El Karoui and M. Mrad}, TITLE = {An Exact Connection between two Solvable SDEs and a Non Linear Utility Stochastic PDEs}, JOURNAL = {preprint.}, YEAR = {2010}, } @article {MRADNEK03, AUTHOR = {N. El Karoui and M. Mrad }, TITLE = {Mixture of consistent Stochastic Utilities, and A priori randomness }, JOURNAL = {preprint.}, YEAR = {2010},} @book {MRAD, AUTHOR = {M. MRAD}, TITLE = {Utilit\'es Progressives Dynamiques}, SERIES = {Thesis}, PUBLISHER = {PASTEL}, YEAR = {2009}, } @incollection {ElKaroui, AUTHOR = {El Karoui, N.}, TITLE = {Les aspects probabilistes du contr\^ole stochastique}, BOOKTITLE = {Ninth {S}aint {F}lour {P}robability {S}ummer {S}chool---1979 ({S}aint {F}lour, 1979)}, SERIES = {Lecture Notes in Math.}, VOLUME = {876}, PAGES = {73--238}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1981}, } @article {MR1802922, AUTHOR = {R. Rouge and N. El Karoui}, TITLE = {Pricing via utility maximization and entropy}, NOTE = {INFORMS Applied Probability Conference (Ulm, 1999)}, JOURNAL = {Math. Finance}, FJOURNAL = {Mathematical Finance. An International Journal of Mathematics, Statistics and Financial Economics}, VOLUME = {10}, YEAR = {2000}, NUMBER = {2}, PAGES = {259--276}, } @article{ve:et, author="Ventzel, A.D.", title="On equations of the theory of conditional {M}arkov processes", journal="Theory of Probability and its Applications", volume=10, pages="357-361", year=1965 } @article {MR2079611, AUTHOR = {Z. H. Wei and S. G. Zhang}, TITLE = {Relationship between optimal growth portfolio and martingale measure}, JOURNAL = {Chinese J. Appl. Probab. Statist.}, FJOURNAL = {Chinese Journal of Applied Probability and Statistics. Yingyong Gail\"u Tongji}, VOLUME = {19}, YEAR = {2003}, NUMBER = {1}, PAGES = {14--18} } @article {Choulli, AUTHOR = {Choulli, Tahir and Stricker, Christophe and Li, Jia}, TITLE = {Minimal {H}ellinger martingale measures of order {$q$}}, JOURNAL = {Finance Stoch.}, FJOURNAL = {Finance and Stochastics}, VOLUME = {11}, YEAR = {2007}, NUMBER = {3}, PAGES = {399--427}, } @article {HMPS, AUTHOR = {Harrison, J. Michael and Pliska, Stanley R.}, TITLE = {Martingales and stochastic integrals in the theory of continuous trading}, JOURNAL = {Stochastic Process. Appl.}, FJOURNAL = {Stochastic Processes and their Applications}, VOLUME = {11}, YEAR = {1981}, NUMBER = {3}, PAGES = {215--260}, }