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

    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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