摘要: We analyze a problem of maximization expected terminal wealth and consumption in markets with some "imperfection", such as constraints on the permitted portfolios, labor income, or/and nonlinearity portfolio dynamics. By using general optional decomposition under multiplicative form, we develop dual formulation. Then, conditions imposed model setting utility functions, are able to prove an existence uniqueness optimal solution primal corresponding by convex duality.
sci-hub.st 参考文章(52)
Bruno Biais, Thomas Björk, Jakša Cvitanić, Nicole El Karoui, Elyés Jouini, Jean Charles Rochet, N El Karoui, MC Quenez, Non-linear pricing theory and backward stochastic differential equations Lecture Notes in Mathematics. pp. 191- 246 ,(1997) , 10.1007/BFB0092001
Norihiko Kazamaki, Continuous Exponential Martingales and Bmo ,(1994)
Ivar Ekeland, Jean Pierre Aubin, Applied Nonlinear Analysis ,(1984)
Claude Dellacherie, Paul André Meyer, Probabilities and potential Hermann , North-Holland Pub. Co , Sole distributors for the U.S. and Canada, Elsevier North-Holland. ,(1978)
Mark Broadie, Jaksa Cvitanic, Halil Mete Soner, Optimal Replication of Contingent Claims under Portfolio Constraints SSRN Electronic Journal. ,(1996) , 10.2139/SSRN.693
Philip E. Protter, Stochastic integration and differential equations : a new approach Springer-Verlag. ,(1990)
Steven E. Shreve, Ioannis Karatzas, Brownian Motion and Stochastic Calculus ,(1987)
John C Cox, Chi-fu Huang, Optimal consumption and portfolio policies when asset prices follow a diffusion process Journal of Economic Theory. ,vol. 49, pp. 33- 83 ,(1989) , 10.1016/0022-0531(89)90067-7
D. O. Kramkov, Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets Probability Theory and Related Fields. ,vol. 105, pp. 459- 479 ,(1996) , 10.1007/BF01191909
D. Kramkov, W. Schachermayer, The asymptotic elasticity of utility functions and optimal investment in incomplete markets Annals of Applied Probability. ,vol. 9, pp. 904- 950 ,(1999) , 10.1214/AOAP/1029962818