Asymptotics and duality for the Davis and Norman problem

References

• Campi , L. and Schachermayer , W. 2006 . A super-replication theorem in Kabanov's model of transaction costs . Finance Stoch. , 10 ( 4 ) : 579 – 596 .
   Web of Science ®Google Scholar
• Constantinides , G. 1986 . Capital market equilibrium with transaction costs . J. Pol. Econ. , 94 : 842 – 862 .
   Web of Science ®Google Scholar
• Cvitanić , J. and Karatzas , I. 1996 . Hedging and portfolio optimization under transaction costs: A martingale approach . Math. Finance , 6 ( 2 ) : 133 – 165 .
   Google Scholar
• Davis , M.H.A. and Norman , A.R. 1990 . Portfolio selection with transaction costs . Math. Oper. Res. , 15 ( 4 ) : 676 – 713 .
   Web of Science ®Google Scholar
• Dumas , B. and Luciano , E. 1991 . An exact solution to a dynamic portfolio choice problem under transaction costs . J. Finance , 46 ( 2 ) : 577 – 595 .
   Web of Science ®Google Scholar
• S. Gerhold, J. Muhle-Karbe, and W. Schachermayer, The dual optimizer for the growth-optimal portfolio under transaction costs, Finance Stoch. To appear (2011)
   Google Scholar
• Goll , T. and Kallsen , J. 2000 . Optimal portfolios for logarithmic utility . Stochastic Process. Appl. , 89 ( 1 ) : 31 – 48 .
   Web of Science ®Google Scholar
• Gould , H.W. 1974 . Coefficient identities for powers of Taylor and Dirichlet series . Amer. Math. Monthly , 81 : 3 – 14 .
   Web of Science ®Google Scholar
• Guasoni , P. , Rásonyi , M. and Schachermayer , W. 2008 . Consistent price systems and face-lifting pricing under transaction costs . Ann. Appl. Probab. , 18 ( 2 ) : 491 – 520 .
   Web of Science ®Google Scholar
• Gunning , R.C. and Rossi , H. 1965 . Analytic Functions of Several Complex Variables , Englewood Cliffs, NJ : Prentice-Hall Inc. .
   Google Scholar
• Ilyashenko , Y. and Yakovenko , S. 2008 . Lectures on Analytic Differential Equations , Graduate Studies in Mathematics Vol. 86 , Providence, RI : American Mathematical Society .
   Google Scholar
• Janeček , K. and Shreve , S.E. 2004 . Asymptotic analysis for optimal investment and consumption with transaction costs . Finance Stoch. , 8 ( 2 ) : 181 – 206 .
   Web of Science ®Google Scholar
• Jouini , E. and Kallal , H. 1995 . Martingales and arbitrage in securities markets with transaction costs . J. Econom. Theory , 66 ( 1 ) : 178 – 197 .
   Web of Science ®Google Scholar
• Kallsen , J. and Muhle-Karbe , J. 2010 . On using shadow prices in portfolio optimization with transaction costs . Ann. Appl. Probab. , 20 ( 4 ) : 1341 – 1358 .
   Web of Science ®Google Scholar
• Karatzas , I. and Shreve , S.E. 1998 . Methods of Mathematical Finance , Applications of Mathematics Vol. 39 , New York : Springer-Verlag .
   Google Scholar
• Kühn , C. and Stroh , M. 2010 . Optimal portfolios of a small investor in a limit order market: A shadow price approach . Math. Finance Econ. , 3 ( 2 ) : 45 – 72 .
   Web of Science ®Google Scholar
• Magill , M.J.P. and Constantinides , G.M. 1976 . Portfolio selection with transactions costs . J. Econom. Theory , 13 ( 2 ) : 245 – 263 .
   Web of Science ®Google Scholar
• Merton , R.C. 1969 . Lifetime portfolio selection under uncertainty: The continuous-time case . Rev. Econ. Statist. , 51 ( 3 ) : 247 – 257 .
   Web of Science ®Google Scholar
• Merton , R.C. 1971 . Optimum consumption and portfolio rules in a continuous-time model . J. Econom. Theory , 3 ( 4 ) : 373 – 413 .
   Web of Science ®Google Scholar
• Merton , R.C. 1990 . Continuous Time Finance , Malden : Blackwell .
   Google Scholar
• Rogers , L.C.G. 2004 . “ Why is the effect of proportional transaction costs ? ” . In Mathematics of Finance , Vol. 351 , 303 – 308 . Providence, RI : Contemp. Math. Amer. Math. Soc. .
   Google Scholar
• Schachermayer , W. 2004 . The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time . Math. Finance , 14 ( 1 ) : 19 – 48 .
   Web of Science ®Google Scholar
• Shreve , S.E. and Soner , H.M. 1994 . Optimal investment and consumption with transaction costs . Ann. Appl. Probab. , 4 ( 3 ) : 609 – 692 .
   Web of Science ®Google Scholar
• Skorokhod , A. 1961 . Stochastic equations for diffusion processes in a bounded region . Theory Probab. Appl. , 6 : 264 – 274 .
   Google Scholar
• Taksar , M. , Klass , M.J. and Assaf , D. 1988 . A diffusion model for optimal portfolio selection in the presence of brokerage fees . Math. Oper. Res. , 13 ( 2 ) : 277 – 294 .
   Web of Science ®Google Scholar
• Whalley , A.E. and Wilmott , P. 1997 . An asymptotic analysis of an optimal hedging model for option pricing with transaction costs . Math. Finance , 7 ( 3 ) : 307 – 324 .
   Web of Science ®Google Scholar