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Dynamic Portfolio Optimization with Looping Contagion Risk

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  • Longjie Jia
  • Martijn Pistorius
  • Harry Zheng

Abstract

In this paper we consider a utility maximization problem with defaultable stocks and looping contagion risk. We assume that the default intensity of one company depends on the stock prices of itself and other companies, and the default of the company induces immediate drops in the stock prices of the surviving companies. We prove that the value function is the unique viscosity solution of the HJB equation. We also perform some numerical tests to compare and analyse the statistical distributions of the terminal wealth of log utility and power utility based on two strategies, one using the full information of intensity process and the other a proxy constant intensity process.

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  • Longjie Jia & Martijn Pistorius & Harry Zheng, 2017. "Dynamic Portfolio Optimization with Looping Contagion Risk," Papers 1710.05168, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1710.05168
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/5717 is not listed on IDEAS
    2. 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.
    3. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515, World Scientific Publishing Co. Pte. Ltd..
    4. Yuanfeng Hou & Xiangrong Jin, 2002. "Optimal Investment With Default Risk," FAME Research Paper Series rp46b, International Center for Financial Asset Management and Engineering.
    5. 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.
    6. Jia-Wen Gu & Wai-Ki Ching & Tak-Kuen Siu & Harry Zheng, 2013. "On pricing basket credit default swaps," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1845-1854, December.
    7. Ying Jiao & Huyên Pham, 2011. "Optimal investment with counterparty risk: a default-density model approach," Finance and Stochastics, Springer, vol. 15(4), pages 725-753, December.
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