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Reflected BSDEs with random default time and related mixed optimal stopping-control problems

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Abstract

In this paper we study the one-dimensional reflected backward stochastic differential equations which are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting. Using a penalization method, we prove the existence and uniqueness of the solutions to these equations. As an application, we show that under proper assumptions the solution of the reflected equation is the value of the related mixed optimal stopping-control problem.

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Authors and Affiliations

  1. School of Economics, Central University of Finance and Economics, Beijing, 100081, China

    Dong-mei Guo

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Dong-mei Guo

  3. Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Xiao-ming Xu

Authors
  1. Dong-mei Guo
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  2. Xiao-ming Xu
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Corresponding author

Correspondence to Xiao-ming Xu.

Additional information

This first author is supported by Humanities and Social Science Research Youth Fund of the Ministry of Education (11YJC790015), Economic and Financial Research Department, National Centre for Mathematics and interdisciplinary Sciences, CAS, and the Innovative Research Team Support Program of Central University of Finance and Economics; The second author is supported by the Mathematical Tianyuan Foundation of China (Grant No. 11126050) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20113207120002).

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Guo, Dm., Xu, Xm. Reflected BSDEs with random default time and related mixed optimal stopping-control problems. Acta Math. Appl. Sin. Engl. Ser. 29, 165–178 (2013). https://doi.org/10.1007/s10255-013-0202-x

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  • DOI: https://doi.org/10.1007/s10255-013-0202-x

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