Title

Completeness Of Security Markets And Backward Stochastic Differential Equations With Unbounded Coefficients

Keywords

Backward stochastic diffrerential equations; Completeness; Exponential super-martingale

Abstract

For a standard Black-Scholes-type security market, completeness is equivalent to the solvability of a linear backward stochastic differential equation (BSDE). When the interest rate is bounded, there exists a bounded risk premium process, and the volatility matrix has certain surjectivity, then the BSDE will be solvable and the market will be complete. However, if the risk premium process and/or the interest rate is not bounded, one gets a BSDE with unbounded coefficients to solve. In this paper, we will discuss such a situation and will present some solvability results for the BSDE which will lead to the completeness of the market. © 2005 Elsevier Ltd. All rights reserved.

Publication Date

11-30-2005

Publication Title

Nonlinear Analysis, Theory, Methods and Applications

Volume

63

Issue

5-7

Number of Pages

-

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.na.2005.02.035

Socpus ID

28044439626 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/28044439626

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