RESEARCH ARTICLE

Optimal portfolio and consumption selection with default risk

  • Lijun BO 1 ,
  • Yongjin WANG 2 ,
  • Xuewei YANG , 3
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  • 1. Department of Mathematics, Xidian University, Xi’an 710071, China
  • 2. School of Business, Nankai University, Tianjin 300071, China
  • 3. School of Management and Engineering, Nanjing University, Nanjing 210093, China

Received date: 25 Oct 2010

Accepted date: 21 May 2012

Published date: 01 Dec 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We investigate an optimal portfolio and consumption choice problem with a defaultable security. Under the goal of maximizing the expected discounted utility of the average past consumption, a dynamic programming principle is applied to derive a pair of second-order parabolic Hamilton-Jacobi- Bellman (HJB) equations with gradient constraints. We explore these HJB equations by a viscosity solution approach and characterize the post-default and pre-default value functions as a unique pair of constrained viscosity solutions to the HJB equations.

Cite this article

Lijun BO , Yongjin WANG , Xuewei YANG . Optimal portfolio and consumption selection with default risk[J]. Frontiers of Mathematics in China, 2012 , 7(6) : 1019 -1042 . DOI: 10.1007/s11464-012-0224-3

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