An optimal portfolio problem in a defaultable market

An optimal portfolio problem in a defaultable market

Lijun Bo, Yongjin Wang, and Xuewei Yang

Source: Adv. in Appl. Probab. Volume 42, Number 3 (2010), 689-705.

Abstract

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.

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Primary Subjects: 93E20, 60H30

Keywords: Portfolio optimization; defaultable security; stochastic factor; Hamilton-Jacobi-Bellman equation; sub/super-solution

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aap/1282924059
Digital Object Identifier: doi:10.1239/aap/1282924059
Zentralblatt MATH identifier: 05820049
Mathematical Reviews number (MathSciNet): MR2779555

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