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Robust Optimal Portfolio Choice Under Markovian Regime-switching Model

Author

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  • Robert J. Elliott

    (University of Calgary
    University of Adelaide)

  • Tak Kuen Siu

    (Curtin University of Technology)

Abstract

We investigate an optimal portfolio selection problem in a continuous-time Markov-modulated financial market when an economic agent faces model uncertainty and seeks a robust optimal portfolio strategy. The key market parameters are assumed to be modulated by a continuous-time, finite-state Markov chain whose states are interpreted as different states of an economy. The goal of the agent is to maximize the minimal expected utility of terminal wealth over a family of probability measures in a finite time horizon. The problem is then formulated as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game between the agent and the market. We solve the problem by the Hamilton-Jacobi-Bellman approach.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:2:d:10.1007_s11009-008-9085-3
    DOI: 10.1007/s11009-008-9085-3
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    1. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482.
    2. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    3. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    4. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Permanent Income and Pricing," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 3, pages 33-81, World Scientific Publishing Co. Pte. Ltd..
    5. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    8. 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..
    9. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    10. 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.
    11. Bong‐Gyu Jang & Hyeng Keun Koo & Hong Liu & Mark Loewenstein, 2007. "Liquidity Premia and Transaction Costs," Journal of Finance, American Finance Association, vol. 62(5), pages 2329-2366, October.
    12. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    Cited by:

    1. Lijun Bo & Huafu Liao & Yongjin Wang, 2018. "Optimal Credit Investment and Risk Control for an Insurer with Regime-Switching," Papers 1807.05513, arXiv.org.
    2. Ivan Guo & Nicolas Langrené & Gregoire Loeper & Wei Ning, 2020. "Robust utility maximization under model uncertainty via a penalization approach," Working Papers hal-02910261, HAL.
    3. Xiang Lin & Chunhong Zhang & Tak Siu, 2012. "Stochastic differential portfolio games for an insurer in a jump-diffusion risk process," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(1), pages 83-100, February.
    4. Zhiping Chen & Xinkai Zhuang & Jia Liu, 2019. "A Sustainability-Oriented Enhanced Indexation Model with Regime Switching and Cardinality Constraint," Sustainability, MDPI, vol. 11(15), pages 1-14, July.
    5. 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.
    6. Chen, Ping & Yam, S.C.P., 2013. "Optimal proportional reinsurance and investment with regime-switching for mean–variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 871-883.
    7. Eduard Baitinger & Christian Fieberg & Thorsten Poddig & Armin Varmaz, 2015. "Liquidity-driven approach to dynamic asset allocation: evidence from the German stock market," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 29(4), pages 365-379, November.
    8. Dong, Yinghui & Yuen, Kam C. & Wu, Chongfeng, 2014. "Unilateral counterparty risk valuation of CDS using a regime-switching intensity model," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 25-35.
    9. Jin-Ray Lu & Chih-Ming Chan, 2014. "Optimal portfolio choice of gold assets in the differential market and differential game structures," Review of Quantitative Finance and Accounting, Springer, vol. 42(2), pages 309-325, February.
    10. Bo, Lijun & Tang, Dan & Wang, Yongjin, 2017. "Optimal investment of variance-swaps in jump-diffusion market with regime-switching," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 175-197.
    11. Liu, Jia & Chen, Zhiping, 2018. "Time consistent multi-period robust risk measures and portfolio selection models with regime-switching," European Journal of Operational Research, Elsevier, vol. 268(1), pages 373-385.

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