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Portfolio optimization with a defaultable security

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  • Tomasz Bielecki
  • Inwon Jang

Abstract

In this paper we derive a closed-form solution for a representative investor who optimally allocates her wealth among the following securities: a credit-risky asset, a default-free bank account, and a stock. Although the inclusion of a credit-related financial product in the portfolio selection is more realistic, no closed-form solutions to date are given in the literature when a recovery value is considered in the event of a default. While most authors have assumed some recovery scheme in their initial model set up, they do not address the portfolio problem with a recovery when a default actually occurs. Given the tractability of the recovery of market value, we solved the optimal portfolio problem for the representative investor whose utility function is a Constant Relative Risk Aversion utility function. We find that the investor will allocate larger fraction of wealth to the defaultable security as long as the default-event risk is priced. These results are very intuitive and reasonable since it indicates that if the default risk premium is not priced properly the investor purchases less defaultable securities. Copyright Springer Science+Business Media, LLC 2006

Suggested Citation

  • Tomasz Bielecki & Inwon Jang, 2006. "Portfolio optimization with a defaultable security," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(2), pages 113-127, June.
    • Handle: RePEc:kap:apfinm:v:13:y:2006:i:2:p:113-127
    DOI: 10.1007/s10690-007-9037-x
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    References listed on IDEAS

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    1. Robert A. Jarrow & David Lando & Fan Yu, 2008. "Default Risk And Diversification: Theory And Empirical Implications," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 19, pages 455-480, World Scientific Publishing Co. Pte. Ltd..
    2. Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
    3. Yuanfeng Hou & Xiangrong Jin, 2002. "Optimal Investment With Default Risk," FAME Research Paper Series rp46b, International Center for Financial Asset Management and Engineering.
    4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    5. Joost Driessen, 2005. "Is Default Event Risk Priced in Corporate Bonds?," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 165-195.
    6. Antje Berndt & Rohan Douglas & Darrell Duffie & Mark Ferguson, "undated". "Measuring Default Risk Premia from Default Swap Rates and EDFs," GSIA Working Papers 2006-E31, Carnegie Mellon University, Tepper School of Business.
    7. Roger Walder, 2002. "Dynamic Allocation of Treasury and Corporate Bond Portfolios," FAME Research Paper Series rp64, International Center for Financial Asset Management and Engineering.
    8. Ralf Korn & Holger Kraft, 2003. "Optimal Portfolios With Defaultable Securities A Firm Value Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(08), pages 793-819.
    9. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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    Cited by:

    1. Agostino Capponi & José Figueroa-López & Andrea Pascucci, 2015. "Dynamic credit investment in partially observed markets," Finance and Stochastics, Springer, vol. 19(4), pages 891-939, October.
    2. Lijun Bo & Xindan Li & Yongjin Wang & Xuewei Yang, 2013. "Optimal Investment and Consumption with Default Risk: HARA Utility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(3), pages 261-281, September.
    3. Agostino Capponi & Lijun Bo, 2016. "Robust Optimization of Credit Portfolios," Papers 1603.08169, arXiv.org.
    4. Zhu, Huiming & Deng, Chao & Yue, Shengjie & Deng, Yingchun, 2015. "Optimal reinsurance and investment problem for an insurer with counterparty risk," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 242-254.
    5. Lijun Bo & Agostino Capponi, 2016. "Optimal Investment under Information Driven Contagious Distress," Papers 1612.06133, arXiv.org.
    6. Deng, Chao & Zeng, Xudong & Zhu, Huiming, 2018. "Non-zero-sum stochastic differential reinsurance and investment games with default risk," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1144-1158.
    7. Agostino Capponi & Jose Figueroa-Lopez & Jeffrey Nisen, 2011. "Pricing and Semimartingale Representations of Vulnerable Contingent Claims in Regime-Switching Markets," Papers 1110.0403, arXiv.org, revised Feb 2012.
    8. Giulia Di Nunno & Steffen Sjursen, 2013. "Information and optimal investment in defaultable assets," Papers 1312.6032, arXiv.org.

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