Completeness of security markets and solvability of linear backward stochastic differential equations

    Authors

    J. M. Yong

    Comments

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    Abbreviated Journal Title

    J. Math. Anal. Appl.

    Keywords

    completeness of market; backward stochastic differential equations; exponential process; 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, for short). An ideal case is that the interest rate is bounded, there exists a bounded risk premium process, and the volatility matrix has certain surjectivity. In this case the corresponding BSDE has bounded coefficients and it is solvable leading to the completeness of the market. However, in general, the risk premium process and/or the interest rate could be unbounded. Then the corresponding BSDE will have unbounded coefficients. For this case, do we still have completeness of the market? The purpose of this paper is to discuss the solvability of BSDEs with possibly unbounded coefficients, which will result in the completeness of the corresponding market. (c) 2005 Elsevier Inc. All rights reserved.

    Journal Title

    Journal of Mathematical Analysis and Applications

    Volume

    319

    Issue/Number

    1

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    333

    Last Page

    356

    WOS Identifier

    WOS:000236943900023

    ISSN

    0022-247X

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