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Exponential Utility Maximization in an Incomplete Market with Defaults

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Exponential Utility Maximization in an Incomplete Market with Defaults
2.	Creator	Author's name, affiliation, country	Thomas Lim; LPMA Université Paris 7-ALMA Research
2.	Creator	Author's name, affiliation, country	Marie-Claire Quenez; LPMA Université Paris 7-INRIA
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Optimal investment; exponential utility; default time; incomplete market; dynamic programming; backward stochastic di
3.	Subject	Subject classification	49L20; 93E20
4.	Description	Abstract	In this paper, we study the exponential utility maximization problem in an incomplete market with a default time inducing a discontinuity in the price of stock. We consider the case of strategies valued in a closed set. Using dynamic programming and BSDEs techniques, we provide a characterization of the value function as the maximal subsolution of a backward stochastic differential equation (BSDE) and an optimality criterium. Moreover, in the case of bounded coefficients, the value function is shown to be the maximal solution of a BSDE. Moreover, the value function can be written as the limit of a sequence of processes which can be characterized as the solutions of Lipschitz BSDEs in the case of bounded coefficients. In the case of convex constraints and under some exponential integrability assumptions on the coefficients, some complementary properties are provided. These results can be generalized to the case of several default times or a Poisson process.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2011-08-10
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/918
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-918
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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