Special Issue for Professor Peter Imkeller's 60th BirthdayNo Access

OPTIMAL CONSUMPTION AND INVESTMENT IN INCOMPLETE MARKETS WITH GENERAL CONSTRAINTS

PATRICK CHERIDITO

Princeton University, Princeton, NJ 08544, USA

Search for more papers by this author

and

YING HU

IRMAR, Université Rennes 1, 35042 Rennes Cedex, France

Search for more papers by this author

https://doi.org/10.1142/S0219493711003280Cited by:29 (Source: Crossref)

Abstract

We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We provide explicit solutions for investors with exponential, logarithmic as well as power utility and show that they are unique if the constraints are convex. Our approach is based on martingale methods that rely on results on the existence and uniqueness of solutions to BSDEs with drivers of quadratic growth.

Keywords:

AMSC: 91G10, 60H10

References

S. Ankirchner, P. Imkeller and A. Popier, Stochastic Process. Appl. 119, 2744 (2009), DOI: 10.1016/j.spa.2009.02.003. Crossref, Web of Science, Google Scholar
P. Briand and Y. Hu, Probab. Th. Relat. Fields 136, 604 (2006), DOI: 10.1007/s00440-006-0497-0. Crossref, Web of Science, Google Scholar
P. Briand and Y. Hu, Probab. Theory Related Fields 141, 543 (2008), DOI: 10.1007/s00440-007-0093-y. Crossref, Web of Science, Google Scholar
P. Cheridito, H. Kawaguchi and M. Maejima, Electron. J. Probab. 8, 14 (2003). Google Scholar
P. Cheridito, M. Kupper and N. Vogelpoth, Conditional analysis on ℝd, preprint (2010) . Google Scholar
F. Delbaen, Y. Hu and A. Richou, On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions, Ann. Inst. Henri Poincaré Probab. Stat., to appear . Google Scholar
Y. Hu, P. Imkeller and M. Müller, Ann. Appl. Probab. 15, 1691 (2005), DOI: 10.1214/105051605000000188. Crossref, Web of Science, Google Scholar
I. Karatzas and S. E. Shreve , Methods of Mathematical Finance ( Springer-Verlag , 1998 ) . Crossref, Google Scholar
N. Kazamaki , Continuous Exponential Martingales and BMO , Lecture Notes in Math 1579 ( Springer-Verlag , 1994 ) . Crossref, Google Scholar
M. Kobylanski, Ann. Probab. 28, 558 (2000), DOI: 10.1214/aop/1019160253. Crossref, Web of Science, Google Scholar
M. A. Morlais, Finance Stoch. 13, 121 (2009), DOI: 10.1007/s00780-008-0079-3. Crossref, Web of Science, Google Scholar
M. Nutz, The Bellman equation for power utility maximization with semimartingales , arXiv:0912.1883 . Google Scholar
E. Pardoux and S. Peng, Syst. Control Lett. 14, 55 (1990), DOI: 10.1016/0167-6911(90)90082-6. Crossref, Web of Science, Google Scholar