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Robust Optimal Investment Strategies with Exchange Rate Risk and Default Risk

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  • Wei Wang

    (School of Mathematics and Statistics, Ningbo University, No. 818 Fenghua Road, Ningbo 315211, China)

  • Qianyan Li

    (School of Mathematics and Statistics, Ningbo University, No. 818 Fenghua Road, Ningbo 315211, China)

  • Quan Li

    (School of Mathematics and Statistics, Ningbo University, No. 818 Fenghua Road, Ningbo 315211, China)

  • Song Xu

    (School of Mathematics and Statistics, Ningbo University, No. 818 Fenghua Road, Ningbo 315211, China)

Abstract

The problem of robust optimal investment with exchange rate risk and default risk is studied. We assume that investors are ambiguity averse and they have access not only to the domestic market but also to the foreign market. The corresponding Hamilton–Jacobi–Bellman (HJB) equations are first obtained through the robust stochastic optimal control theory. Then, we discuss the optimal investment problems before and after default, and the value functions and optimal investment strategies are obtained. Finally, we find that the optimal investment strategies of pre-default are affected by the intensity of default and the credit spread, and the investors cannot hold defaultable bonds in the post-default case. Numerical results also show that the exchange rate risk, default risk and ambiguity aversion have a great effect on the optimal investment strategies.

Suggested Citation

  • Wei Wang & Qianyan Li & Quan Li & Song Xu, 2023. "Robust Optimal Investment Strategies with Exchange Rate Risk and Default Risk," Mathematics, MDPI, vol. 11(6), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1550-:d:1104326
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    References listed on IDEAS

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    1. Zheng, Xiaoxiao & Zhou, Jieming & Sun, Zhongyang, 2016. "Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 77-87.
    2. Hening Liu, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Post-Print hal-00781344, HAL.
    3. Shian‐Chang Huang & Mao‐Wei Hung, 2005. "Pricing foreign equity options under Lévy processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(10), pages 917-944, October.
    4. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    5. Robert J. Elliott & Tak Kuen Siu, 2009. "Robust Optimal Portfolio Choice Under Markovian Regime-switching Model," Methodology and Computing in Applied Probability, Springer, vol. 11(2), pages 145-157, June.
    6. Chen Fei & Weiyin Fei & Yayun Rui & Litan Yan, 2021. "International investment with exchange rate risk," Asia-Pacific Journal of Accounting & Economics, Taylor & Francis Journals, vol. 28(2), pages 225-241, March.
    7. Escobar, Marcos & Ferrando, Sebastian & Rubtsov, Alexey, 2015. "Robust portfolio choice with derivative trading under stochastic volatility," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 142-157.
    8. Kaushik I. Amin & Robert A. Jarrow, 2008. "Pricing foreign currency options under stochastic interest rates," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 14, pages 307-326, World Scientific Publishing Co. Pte. Ltd..
    9. Chang Guo & Xiaoyang Zhuo & Corina Constantinescu & Olivier Menoukeu Pamen, 2018. "Optimal Reinsurance-Investment Strategy Under Risks of Interest Rate, Exchange Rate and Inflation," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1477-1502, December.
    10. Zeng, Yan & Li, Danping & Chen, Zheng & Yang, Zhou, 2018. "Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 88(C), pages 70-103.
    11. Liu, Hening, 2011. "Dynamic portfolio choice under ambiguity and regime switching mean returns," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 623-640, April.
    12. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," The Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    13. Lars Peter Hansen & Thomas J Sargent, 2014. "A Quartet of Semigroups for Model Specification, Robustness, Prices of Risk, and Model Detection," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 4, pages 83-143, World Scientific Publishing Co. Pte. Ltd..
    14. Branger, Nicole & Larsen, Linda Sandris, 2013. "Robust portfolio choice with uncertainty about jump and diffusion risk," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5036-5047.
    15. 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.
    16. Zhongyang Sun & Junyi Guo, 2018. "Optimal mean–variance investment and reinsurance problem for an insurer with stochastic volatility," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(1), pages 59-79, August.
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