Title

Completeness of security markets and backward stochastic differential equations with unbounded coefficients

Authors

Authors

J. Yong

Comments

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Abbreviated Journal Title

Nonlinear Anal.-Theory Methods Appl.

Keywords

Completeness; Backward stochastic differential equations; Exponential; super-martingale; Mathematics, Applied; Mathematics

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. (C) 2005 Elsevier Ltd. All rights reserved.

Journal Title

Nonlinear Analysis-Theory Methods & Applications

Volume

63

Issue/Number

5-7

Publication Date

1-1-2005

Document Type

Article

Language

English

First Page

E2079

Last Page

E2089

WOS Identifier

WOS:000208147800205

ISSN

0362-546X

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