Portfolio optimization in a Lévy market with intertemporal substitution and transaction costs

References

• Akian , M. , Menaldi , I.L. and Sulem , A. 1996 . “On an investment-consumption model with transaction costs” . SIAM J. Control Optim. , 34 (1) : 329 – 364 .
   Web of Science ®Google Scholar
• Alvarez , O. 1994 . “A singular stochastic control problem in an unbounded domain” . Comm. Partial Differ. Eqs. , 19 (11-12) : 2075 – 2089 .
   Web of Science ®Google Scholar
• Alvarez , O. and Tourin , A. 1996 . “Viscosity solutions of nonlinear integro-differential equations” . Ann. Inst. H. Poincaré Anal. Non Linéaire , 13 (3) : 293 – 317 .
   Google Scholar
• Bank , P. and Riedel , F. 2001 . 'Optimal consumption choice under uncertainty with intertemporal substitution” . Ann. Appl. Prob. , 11 (3) : 750 – 788 .
   Web of Science ®Google Scholar
• Barles , G. , Buckdahn , R. and Pardoux , E. 1997 . “Backward stochastic differential equations and integral-partial differential equations” . Stochast. Stochast. Rep. , 60 (1-2) : 57 – 83 .
   Google Scholar
• Barndorff-Nielsen , O.E. 1977 . “Exponentially decreasing distributions for the logarithm of particle size” . Pmc. R. Soc. London Ser. A , 353 : 401 – 419 .
   Web of Science ®Google Scholar
• Barndorff-Nielsen , O.E. 1998 . “Processes of normal inverse Gaussian type” . Finance Stochast. , 2 : 41 – 68 .
   Google Scholar
• Benth , P.E. , Karlsen , K.H. and Reikvam , K. 2001 . “Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: a viscosity solution approach” . Finance Stochast. , 3 : 275 – 303 .
   Google Scholar
• Benth , P.E. , Karlsen , K.H. and Reikvam , K. 2001 . “Optimal portfolio management rules in a non- Gaussian market with durability and intertemporal substitution” . Finance Stochast. , 4 : 447 – 467 .
   Google Scholar
• Benth , P.E. , Karlsen , K.H. and Reikvam , K. 2001 . “A note on portfolio management under non- Gaussian logreturns” . Int. J. Theor. Appl. Finance , 4 (5) : 711 – 731 .
   Google Scholar
• Benth , P.E. , Karlsen , K.H. and Reikvam , K. "On the existence of optimal controls for a singular stochastic control problem in finance" . Proceedings of the Workshop on Mathematical Finance in Konstanz . 2000 , Germany. pp. 79 – 88 . Basel : (Birkhäuser .
   Google Scholar
• Bertoin , J. 1996 . Levy Processes Cambridge Tracts in Mathematics , Vol. 121 , Cambridge : Cambridge University Press .
   Google Scholar
• Crandall , M.G. , Evans , L.C. and Lions , P.-L. 1984 . “Some properties of viscosity solutions of Hamilton-Jacobi equations” . Trans. Am. Math. Soc. , 282 (2) : 487 – 502 .
   Web of Science ®Google Scholar
• Crandall , M.G. , Ishii , H. and Lions , P.-L . 1992 . “User's guide to viscosity solutions of second order partial differential equations” . Bull. Am. Math. Soc. (N.S.) , 27 (1) : 1 – 67 .
   Web of Science ®Google Scholar
• Crandall , M.G. and Lions , P.-L . 1983 . “Viscosity solutions of Hamilton-Jacobi equations” . Trans. Am. Math. Soc. , 277 (1) : 1 – 42 .
   Web of Science ®Google Scholar
• Damgaard , A. “Optimal Portfolio Choice and Utility Based Option Pricing in Markets with Transaction Costs” . Odense : University of Southern Denmark . Ph.D. Thesis
   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
• Davis , M.H.A. , Panas , V.G. and Zariphopoulou , T. 1993 . “European option pricing with transaction costs” . SIAM J. Control Optim. , 31 (2) : 470 – 493 .
   Web of Science ®Google Scholar
• Capuzzo-Dolcetta , I. and Lions , P.-L. 1990 . “Hamilton-Iacobi equations with state constraints” . Trans. Am. Math. Soc. , 318 (2) : 643 – 683 .
   Web of Science ®Google Scholar
• Eberlein , E. and Keller , U. 1995 . “Hyperbolic distributions in finance” . Bernoulli , 1 (3) : 281 – 299 .
   Google Scholar
• Fleming , W.H. and Soner , H.M. 1993 . Controlled Markov Processes and Viscosity Solutions , Berlin : Springer .
   Google Scholar
• Framstad , N.C. , Øksendal , B. Sulem , A. 'Optimal consumption and portfolio in a jump diffusion market" . Workshop on Mathematical Finance . Edited by: Shiryaev , A. pp. 9 – 20 . Paris : INRIA .
   Google Scholar
• Framstad , N.C. , Øksendal , B. and Sulem , A. 2001 . “Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs” . J. Math. Econ , 35 : 233 – 257 .
   Web of Science ®Google Scholar
• Gerber , H. and Shiu , E. 1994 . “Option pricing with Esscher transform” . Trans. Soc. Actuaries , 46 : 91 – 191 .
   Google Scholar
• Hindy , A. and Huang , C. 1992 . “Intertemporal preferences for uncertain consumption: a continuous time approach” . Econometrica , 60 (4) : 781 – 801 .
   Web of Science ®Google Scholar
• Hindy , A. and Huang , C. 1993 . 'Optimal consumption and portfolio rules with durability and local substitution” . Econometrica , 61 : 85 – 122 .
   Web of Science ®Google Scholar
• Hindy , A. , Huang , C. and Kreps , D. 1992 . “Qn intertemporal preferences in continuous time: the case of certainty” . J. Math. Econ. , 21 (5) : 401 – 440 .
   Web of Science ®Google Scholar
• Hindy , A. , Huang , C. and Zhu , H. 1997 . “Numerical analysis of a free-boundary singular control problem in financial economics” . J. Econ. Dyn. Control , 21 : 297 – 327 .
   Web of Science ®Google Scholar
• Ikeda , N. and Watanabe , S. 1981 . Stochastic Differential Equations and Diffusion Processes , Amsterdam/New York : North-Holland/Kodansha .
   Google Scholar
• Ishii , H. and Lions , R-L. 1990 . “Viscosity solutions of fully nonlinear second-order elliptic partial differential equations” . J. Differ. Eqs. , 83 (1) : 26 – 78 .
   Web of Science ®Google Scholar
• Kallsen , J. 2000 . “Optimal portfolios for exponential Levy processes” . Math. Methods Oper. Res. , 51 : 357 – 374 .
   Web of Science ®Google Scholar
• Katsoulakis , M.A. 1994 . “Viscosity solutions of second order fully nonlinear elliptic equations with state constraints” . Indiana Univ. Math. J. , 43 (2) : 493 – 519 .
   Web of Science ®Google Scholar
• Lasry , J.-M. and Lions , P.-L. 1989 . “Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. I. The model problem” . Math. Ann. , 283 (4) : 583 – 630 .
   Web of Science ®Google Scholar
• Lions , P.L. 1983 . “Optimal control of diffusion processes and Hamilton-Iacobi-Bellman equations. II. Viscosity solutions and uniqueness” . Comm. Partial Differ. Eqs. , 8 (11) : 1229 – 1276 .
   Web of Science ®Google Scholar
• Mandelbrot , B. 1963 . “The variation of certain speculative prices” . J. Business , 36 : 394 – 419 .
   Web of Science ®Google Scholar
• Merton , R.C. 1971 . “Optimum consumption and portfolio rules in a continuous-time model” . J. Econ. Theory , 3 : 373 – 413 .
   Web of Science ®Google Scholar
• 1973 . Erratum , 6 : 213 – 214 .
   Google Scholar
• Pham , H. 1998 . “Optimal stopping of controlled jump diffusion processes: a viscosity solution approach” . J. Math. Syst. Estin. Control , 8 (1) : 27
   Google Scholar
• Prause , K. 1997 . “Modelling financial data using generalized hyperbolic distributions” . Universität Freiburg . Preprint
   Google Scholar
• Plotter , R . 1990 . Stochastic Integration and Differential Equations. A New Approach Applications of Mathematics , Vol. 21 , Berlin : Springer .
   Google Scholar
• Rydberg , TH. 1997 . “The normal inverse Gaussian Levy process: simulation and approximation” . Commun. Statist-Stochastic Models , 13 (4) : 887 – 910 .
   Google Scholar
• Sato , K. 1999 . Levy Processes and Infinitely Divisible Distributions , Cambridge Studies in Advanced Mathematics Vol. 68 , Cambridge : Cambridge University Press .
   Google Scholar
• Sayah , A. 1991 . “Équations d'Hamilton-Jacobi du premier ordre avec termes intégro- différentiels. I. Unicité des solutions de viscosité” . Comm. Partial Differ. Eqs. , 16 (6-7) : 1057 – 1074 .
   Google Scholar
• Sayah , A. 1991 . “Équations d'Hamilton-Jacobi du premier ordre avec termes intégro- différentiels. II. Existence de solutions de viscosité” . Comm. Partial Differ. Eqs. , 16 (6-7) : 1075 – 1093 .
   Google Scholar
• Shreve , S.E. and Soner , H.M. 1994 . 'Optimal investment and consumption with transaction costs” . Ann. Appl. Probab. , 4 (3) : 609 – 692 .
   Google Scholar
• Shreve , S.E. , Soner , H.M. and Cvitanic , I. 1995 . “There is no nontrivial hedging portfolio for option pricing with transaction costs” . Ann. Appl Probab. , 5 (2) : 327 – 355 .
   Google Scholar
• Soner , H.M. 1986 . “Optimal control with state-space constraint. I” . SIAM J. Control Optim. , 24 (3) : 552 – 561 .
   Web of Science ®Google Scholar
• Soner , H.M. 1986 . “Optimal control with state-space constraint. IT . SIAMJ. Control Optim. , 24 (6) : 1110 – 1122 .
   Web of Science ®Google Scholar
• Soner , H.M. 1988 . “Optimal control of jump-Markov processes and viscosity solutions” . In Stochastic Differential Systems, Stochastic Control Theory and Applications , 501 – 511 . Minneapolis, Minn. : Springer . 1986, New York
   Google Scholar
• Zariphopoulou , T. 1992 . “Investment-consumption models with transaction fees and Markovchain parameters” . SIAM J. Control Optim. , 30 (3) : 613 – 636 .
   Web of Science ®Google Scholar
• Tourin , A. and Zariphopoulou , T. 1994 . “Numerical schemes for investment models with singular transactions” . Comput. Econ. , 7 (4) : 287 – 307 .
   Google Scholar
• Zariphopoulou , T. "Transaction costs in portfolio management and derivative pricing" . Introduction to Mathematical Finance Proc. Sympos. Appl. Math. Vol. 57 , pp. 101 – 163 . Providence, RI : Am. Math. Soc. .
   Google Scholar
• Zhu , S. 1991 . “Dynamic Programming and Variational Inequalities in Singular Stochastic Control” . Division of Applied Mathematics, Brown University . Doctoral Dissertation
   Google Scholar