Frontiers of Mathematics in China >
Optimal portfolio and consumption selection with default risk
Received date: 25 Oct 2010
Accepted date: 21 May 2012
Published date: 01 Dec 2012
Copyright
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.
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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