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On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy

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  • Robert Elliott
  • Tak Siu

Abstract

We consider a risk minimization problem in a continuous-time Markovian regime-switching financial model modulated by a continuous-time, observable and finite-state Markov chain whose states represent different market regimes. We adopt a particular form of convex risk measure, which includes the entropic risk measure as a particular case, as a measure of risk. The risk-minimization problem is formulated as a Markovian regime-switching version of a two-player, zero-sum stochastic differential game. One important feature of our model is to allow the flexibility of controlling both the diffusion process representing the financial risk and the Markov chain representing macro-economic risk. This is novel and interesting from both the perspectives of stochastic differential game and stochastic control. A verification theorem for the Hamilton-Jacobi-Bellman (HJB) solution of the game is provided and some particular cases are discussed. Copyright Springer Science+Business Media, LLC 2010

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  • Robert Elliott & Tak Siu, 2010. "On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy," Annals of Operations Research, Springer, vol. 176(1), pages 271-291, April.
    • Handle: RePEc:spr:annopr:v:176:y:2010:i:1:p:271-291:10.1007/s10479-008-0448-5
    DOI: 10.1007/s10479-008-0448-5
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    5. Chevallier Julien & Goutte Stéphane, 2017. "On the estimation of regime-switching Lévy models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(1), pages 3-29, February.
    6. 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.
    7. Kai Zheng & Weidong Xu & Xili Zhang, 2023. "Multivariate Regime Switching Model Estimation and Asset Allocation," Computational Economics, Springer;Society for Computational Economics, vol. 61(1), pages 165-196, January.
    8. Emel Savku, 2023. "A Stochastic Control Approach for Constrained Stochastic Differential Games with Jumps and Regimes," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
    9. Mazin Al Janabi, 2013. "Optimal and coherent economic-capital structures: evidence from long and short-sales trading positions under illiquid market perspectives," Annals of Operations Research, Springer, vol. 205(1), pages 109-139, May.
    10. Levy, Moshe & Kaplanski, Guy, 2015. "Portfolio selection in a two-regime world," European Journal of Operational Research, Elsevier, vol. 242(2), pages 514-524.
    11. Han, Jinhui & Ma, Guiyuan & Yam, Sheung Chi Phillip, 2022. "Relative performance evaluation for dynamic contracts in a large competitive market," European Journal of Operational Research, Elsevier, vol. 302(2), pages 768-780.
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    13. Marco Bonomelli & Rosella Giacometti & Sergio Ortobelli Lozza, 2020. "Joint tails impact in stochastic volatility portfolio selection models," Annals of Operations Research, Springer, vol. 292(2), pages 833-848, September.
    14. Lirong Cui & Quan Zhang & Dejing Kong, 2016. "Some New Concepts and Their Computational Formulae in Aggregated Stochastic Processes with Classifications Based on Sojourn Times," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 999-1019, December.
    15. Jakub Trybu{l}a & Dariusz Zawisza, 2014. "Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences-Stochastic Factor Case," Papers 1403.3212, arXiv.org, revised Jan 2020.
    16. Jakub Trybuła & Dariusz Zawisza, 2019. "Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 966-987, August.
    17. Robert Cox Merton & Francisco Venegas-Martínez, 2021. "Financial Science Trends and Perspectives: A Review Article," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 16(1), pages 1-15, Enero - M.
    18. Gurjeet Dhesi & Bilal Shakeel & Marcel Ausloos, 2021. "Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach," Annals of Operations Research, Springer, vol. 299(1), pages 1397-1410, April.
    19. Ramesh Adhikari & Kyle J. Putnam & Humnath Panta, 2020. "Robust Optimization-Based Commodity Portfolio Performance," IJFS, MDPI, vol. 8(3), pages 1-16, September.
    20. Siyu Lv & Zhen Wu & Qing Zhang, 2022. "The Dynkin game with regime switching and applications to pricing game options," Annals of Operations Research, Springer, vol. 313(2), pages 1159-1182, June.

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