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Dynamic Portfolio Optimization with a Defaultable Security and Regime Switching

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  • Agostino Capponi
  • Jose E. Figueroa-Lopez

Abstract

We consider a portfolio optimization problem in a defaultable market with finitely-many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market coefficients are assumed to depend on the market regime in place, which is modeled by a finite state continuous time Markov process. We rigorously deduce the dynamics of the defaultable bond price process in terms of a Markov modulated stochastic differential equation. Then, by separating the utility maximization problem into the pre-default and post-default scenarios, we deduce two coupled Hamilton-Jacobi-Bellman equations for the post and pre-default optimal value functions and show a novel verification theorem for their solutions. We obtain explicit optimal investment strategies and value functions for an investor with logarithmic utility. We finish with an economic analysis in the case of a market with two regimes and homogenous transition rates, and show the impact of the default intensities and loss rates on the optimal strategies and value functions.

Suggested Citation

  • Agostino Capponi & Jose E. Figueroa-Lopez, 2011. "Dynamic Portfolio Optimization with a Defaultable Security and Regime Switching," Papers 1105.0042, arXiv.org, revised Sep 2011.
    • Handle: RePEc:arx:papers:1105.0042
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    References listed on IDEAS

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    1. Giuseppe Di Graziano & L. C. G. Rogers, 2009. "Equity with Markov-modulated dividends," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 19-26.
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    Cited by:

    1. Liang, Xue & Wang, Guojing, 2012. "On a reduced form credit risk model with common shock and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 567-575.
    2. Yaacov Kopeliovich & Michael Pokojovy & Julia Bernatska, 2024. "On Merton's Optimal Portfolio Problem with Sporadic Bankruptcy for Isoelastic Utility," Papers 2403.15923, arXiv.org, revised Nov 2024.
    3. Longjie Jia & Martijn Pistorius & Harry Zheng, 2017. "Dynamic Portfolio Optimization with Looping Contagion Risk," Papers 1710.05168, arXiv.org, revised Aug 2018.

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