Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MINIMAL AND MAXIMAL BOUNDED SOLUTIONS FOR QUADRATIC BSDES WITH STOCHASTIC CONDITIONS

  • Fan, Shengjun (School of Mathematics China University of Mining and Technology) ;
  • Luo, Huanhuan (School of Mathematics China University of Mining and Technology)
  • Received : 2016.09.13
  • Accepted : 2016.12.26
  • Published : 2017.11.30
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Abstract

This paper is devoted to the minimal and maximal bounded solutions for general time interval quadratic backward stochastic differential equations with stochastic conditions. A general existence result is established by the method of convolution, the exponential transform, Girsanov's transform and a priori estimates, where the terminal time is allowed to be finite or infinite, and the generator g is allowed to have a stochastic semi-linear growth and a general growth in y, and a quadratic growth in z. This improves some existing results at some extent. Some new ideas and techniques are also applied to prove it.

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References

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