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Portfolio optimization with a defaultable security

  • Tomasz Bielecki

    ()

  • Inwon Jang

    ()

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    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

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    File URL: http://hdl.handle.net/10.1007/s10690-007-9037-x
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    Article provided by Springer in its journal Asia-Pacific Financial Markets.

    Volume (Year): 13 (2006)
    Issue (Month): 2 (June)
    Pages: 113-127

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    Handle: RePEc:kap:apfinm:v:13:y:2006:i:2:p:113-127
    Contact details of provider: Web page: http://springerlink.metapress.com/link.asp?id=102851

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    1. Robert A. Jarrow & David Lando & Fan Yu, 2005. "Default Risk And Diversification: Theory And Empirical Implications," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 1-26.
    2. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Roger Walder, 2002. "Dynamic Allocation of Treasury and Corporate Bond Portfolios," FAME Research Paper Series rp64, International Center for Financial Asset Management and Engineering.
    4. Antje Berndt & Rohan Douglas & Darrell Duffie & Mark Ferguson & David Schranz, 2005. "Measuring default risk premia from default swap rates and EDFs," BIS Working Papers 173, Bank for International Settlements.
    5. Joost Driessen, 2005. "Is Default Event Risk Priced in Corporate Bonds?," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 165-195.
    6. 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.
    7. Yuanfeng Hou & Xiangrong Jin, 2002. "Optimal Investment With Default Risk," FAME Research Paper Series rp46b, International Center for Financial Asset Management and Engineering.
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