Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SOLVABILITY OF GENERAL BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS

  • Received : 2011.08.12
  • Published : 2012.11.01
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Abstract

In this paper we study the unique solvability of backward stochastic Volterra integral equations (BSVIEs in short), in terms of both the adapted M-solutions introduced in [19] and the adapted solutions via a new method. A general existence and uniqueness of adapted M-solutions is proved under non-Lipschitz conditions by virtue of a briefer argument than the ones in [13] and [19], which modifies and extends the results in [13] and [19] respectively. For the adapted solutions, the unique solvability of BSVIEs under more general stochastic non-Lipschitz conditions is shown, which improves and generalizes the results in [7], [14] and [15].

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References

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