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An optimal portfolio problem in a defaultable market

Part of: Stochastic systems and control Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Lijun Bo ,
Yongjin Wang  and
Xuewei Yang
Lijun Bo*
Affiliation:
Xidian University
Yongjin Wang*
Affiliation:
Nankai University
Xuewei Yang*
Affiliation:
Nankai University
*
∗ Postal address: Department of Mathematics, Xidian University, Xi'an 710071, P. R. China.
∗∗ Postal address: School of Business, Nankai University, Tianjin 300071, P. R. China.
∗∗∗ Postal address: School of Mathematical Sciences and TEDA Institute of Computational Finance, Nankai University, Tianjin 300071, P. R. China. Email address: xwyangnk@yahoo.com.cn
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Abstract

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We consider a portfolio optimization problem in a defaultable market. The investor can dynamically choose a consumption rate and allocate his/her wealth among three financial securities: a defaultable perpetual bond, a default-free risky asset, and a money market account. Both the default risk premium and the default intensity of the defaultable bond are assumed to rely on some stochastic factor which is described by a diffusion process. The goal is to maximize the infinite-horizon expected discounted log utility of consumption. We apply the dynamic programming principle to deduce a Hamilton-Jacobi-Bellman equation. Then an optimal Markov control policy and the optimal value function is explicitly presented in a verification theorem. Finally, a numerical analysis is presented for illustration.

Keywords

Portfolio optimizationdefaultable securitystochastic factorHamilton-Jacobi-Bellman equationsub/super-solution

MSC classification

Primary: 93E20: Optimal stochastic control 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 3 , September 2010 , pp. 689 - 705
Copyright
Copyright © Applied Probability Trust 2010 

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