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Portfolio optimization in stochastic markets

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  • U. Çakmak
  • S. Özekici

Abstract

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure. Copyright Springer-Verlag 2006

Suggested Citation

  • U. Çakmak & S. Özekici, 2006. "Portfolio optimization in stochastic markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 151-168, February.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:1:p:151-168
    DOI: 10.1007/s00186-005-0020-x
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    Cited by:

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    2. Celikyurt, U. & Ozekici, S., 2007. "Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach," European Journal of Operational Research, Elsevier, vol. 179(1), pages 186-202, May.
    3. İ. Altınel & Bora Çekyay & Orhan Feyzioğlu & M. Keskin & Süleyman Özekici, 2011. "Mission-Based Component Testing for Series Systems," Annals of Operations Research, Springer, vol. 186(1), pages 1-22, June.
    4. Benjamín Vallejo Jiménez & Francisco Venegas Martínez, 2017. "Optimal consumption and portfolio rules when the asset price is driven by a time-inhomogeneous Markov modulated fractional Brownian motion with," Economics Bulletin, AccessEcon, vol. 37(1), pages 314-326.
    5. Reza Keykhaei, 2020. "Portfolio selection in a regime switching market with a bankruptcy state and an uncertain exit-time: multi-period mean–variance formulation," Operational Research, Springer, vol. 20(3), pages 1231-1254, September.
    6. Robert Cox Merton & Francisco Venegas-Martínez, 2021. "Tendencias y perspectivas de la ciencia financiera: Un artículo de revisión," 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.
    7. Chen, Zhiping & Li, Gang & Zhao, Yonggan, 2014. "Time-consistent investment policies in Markovian markets: A case of mean–variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 293-316.
    8. 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.
    9. Huiling Wu, 2016. "Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-17, July.
    10. Zhang, Ling & Zhang, Hao & Yao, Haixiang, 2018. "Optimal investment management for a defined contribution pension fund under imperfect information," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 210-224.
    11. Çanakoglu, Ethem & Özekici, Süleyman, 2010. "Portfolio selection in stochastic markets with HARA utility functions," European Journal of Operational Research, Elsevier, vol. 201(2), pages 520-536, March.
    12. Zeng, Yan & Li, Zhongfei & Lai, Yongzeng, 2013. "Time-consistent investment and reinsurance strategies for mean–variance insurers with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 498-507.
    13. Xiangyu Cui & Jianjun Gao & Yun Shi, 2021. "Multi-period mean–variance portfolio optimization with management fees," Operational Research, Springer, vol. 21(2), pages 1333-1354, June.
    14. Bian, Lihua & Li, Zhongfei & Yao, Haixiang, 2018. "Pre-commitment and equilibrium investment strategies for the DC pension plan with regime switching and a return of premiums clause," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 78-94.
    15. Wu, Huiling & Li, Zhongfei, 2012. "Multi-period mean–variance portfolio selection with regime switching and a stochastic cash flow," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 371-384.
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    17. Ethem Çanakoğlu & Süleyman Özekici, 2009. "Portfolio selection in stochastic markets with exponential utility functions," Annals of Operations Research, Springer, vol. 166(1), pages 281-297, February.

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