Optimal consumption from investment and random endowment in incomplete semimartingale markets

Annals of Probability

Volumn 31, Issue 4, 2003, Pages 1821-1858

  Karatzas, Ioannis ^a   Žitković, Gordan ^a  

^a Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

Convex duality; Finitely additive measures; Incomplete markets; Random endowment; Stochastic processes; Utility maximization

Indexed keywords

EID: 0346332487     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1068646367     Document Type: Article

References (40)

1. BHASKARA RAO, K. P. S. and BHASKARA RAO, M. (1983). Theory of Charges. Academic Press, London.
2. 0(Ω, F, P). Séminaire de Probabilités XXXIII. Lecture Notes in Math. 1709 349-354. Springer, Berlin.
3. CHUNG, K.-L. (1974). A Course in Probability Theory, 2nd ed. Academic Press, New York.
4. Cox, J. C. and HUANG, C. F. (1989). Optimal consumption and portfolio policies when asset prices follow a diffusion process. J. Econom. Theory 49 33-83.
5. Cox, J. C. and HUANG, C. F. (1991). A variational problem arising in financial economics. J. Math. Econom. 20 465-487.
6. Cuoco, D. (1997). Optimal consumption and equilibrium prices with portfolio constraints and stochastic income. J. Econom. Theory 72 33-73.
7. CVITANIĆ, J. and KARATZAS, I. (1992). Convex duality in constrained portfolio optimization. Ann. Appl. Probab. 2 767-818.
8. CVITANIĆ, J., SCHACHERMAYER, W. and WANG, H. (2001). Utility maximization in incomplete markets with random endowment. Finance Stoch. 5 237-259.
9. DELBAEN, F. and SCHACHERMAYER, W. (1993). A general version of the fundamental theorem of asset pricing. Math. Ann. 300 463-520.
10. DELBAEN, F. and SCHACHERMAYER, W. (1995). The existence of absolutely continuous local martingale measures. Ann. Appl. Probab. 5 926-945.
11. DELBAEN, F. and SCHACHERMAYER, W. (1998). The fundamental theorem of asset pricing for unbounded stochastic processes. Math. Ann. 312 215-250.
12. DELBAEN, F. and SCHACHERMAYER, W. (1999). A compactness principle for bounded sequences of martingales with applications. In Proceedings of the Seminar on Stochastic Analysis, Random Fields and Applications 137-173. Birkhäuser, Basel.
13. DELLACHERIE, C. and MEYER, P.-A. (1982). Probabilities and Potential, Vol. B: Theory of Martingales. North-Holland, Amsterdam.
14. EL KAROUI, N. and JEANBLANC-PICQUÉ, M. (1998). Optimization of consumption with labor income. Finance Stoch. 2 409-440.
15. EL KAROUl, N. and QUENEZ, M.-C. (1995). Dynamic programming and pricing of contingent claims in an incomplete market. SIAM J. Control Optim. 33 29-66.
16. FÖLLMER, H. and KRAMKOV, D. (1997). Optional decomposition under constraints. Probab. Theory Related Fields 109 1-25.
17. HE, H. and PEARSON, N. D. (1991). Consumption and portfolio policies with incomplete markets and short-sale constraints: The finite-dimensional case. Math. Finance 1 1-10.
18. HE. H. and PEARSON, N. D. (1991). Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite-dimensional case. J. Econom. Theory 54 259-304.
19. JACOD, J. (1979). Calcul stochastique et problémes de martingales. Lecture Notes in Math. 714. Springer, Berlin.
20. KARATZAS, I. and SHREVE, S. E. (1991). Brownian Motion and Stochastic Calculus, 2nd ed. Springer, New York.
21. KARATZAS, I. and SHREVE, S. E. (1998). Methods of Mathematical Finance. Springer, New York.
22. KARATZAS, I., LEHOCZKY, J. P. and SHREVE, S. E. (1987). Optimal portfolio and consumption decisions for a "small investor" on a finite horizon. SIAM J. Control Optim. 25 1557-1586.
23. KARATZAS, I., LEHOCZKY, J. P., SHREVE, S. E. and Xu, G. L. (1991). Martingale and duality methods for utility maximization in an incomplete market. SIAM J. Control Optim. 29 702-730.
24. KOMLÓS, J. (1967). A generalization of a problem of Steinhaus. Acta Math. Hungar. 18 217-229.
25. KRAMKOV, D. (1996). Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets. Probab. Theory Related Fields 105 459-479.
26. KRAMKOV, D. and SCHACHERMAYER, W. (1999). A condition on the asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9 904-950.
27. LAKNER, P. and SLUD, E. (1991). Optimal consumption by a bond investor: The case of random interest rate adapted to a point process. SIAM J. Control Optim. 29 638-655.
28. MERTON, R. C. (1969). Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economic Statistics 51 247-257.
29. MERTON, R. C. (1971). Optimum consumption and portfolio rules in a conitinuous-time model. J. Econom. Theory 3 373-413.
30. PLISKA, S. R. (1986). A stochastic calculus model of continuous trading: Optimal portfolio. Math. Oper. Res. 11 371-382.
31. PROTTER, PH. (1990). Stochastic Integration and Differential Equations. Springer, New York.
32. ROCKAFELLAR, R. T. (1970). Convex Analysis. Princeton Univ. Press.
33. SCHACHERMAYER, W. (2000). Optimal investment in incomplete financial markets. In Proceedings of the First World Congress of the Bachelier Society 427-462. Springer, Berlin.
34. SCHWARTZ, M. (1986). New proofs of a theorem of Komlós. Acta Math. Hungar. 47 181-185.
35. SHIRYAEV, A. N. (1996). Probability, 2nd ed. Springer, New York. [Translated from the first (1980) Russian edition by R. P. Boas.]
36. STRASSER, H. (1985). Mathematical Theory of Statistics, de Gruyter, Berlin.
37. WOJATSZCYK, P. (1996). Banach Spaces for Analysts. Cambridge Univ. Press.
38. XU, G.-L. (1990). A duality method for optimal consumption and investment under short-selling prohibition. Ph.D. dissertation, Dept. Mathematics, Carnegie-Mellon Univ.
39. YOSIDA, K. and HEWITT, E. (1952). Finitely additive measures. Trans. Amer. Math. Soc. 72 46-66.
40. ŽITKOVIĆ, G. (2002). A filtered version of the bipolar theorem of Brannath and Schacher-mayer. J. Theoret. Probab. 15 41-61.