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Optimal portfolio selection when stock prices follow an jump-diffusion process

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  • Wenjing Guo
  • Chengming Xu

Abstract

A portfolio selection problem in which the prices of stocks follow jump-diffusion process is studied. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. A stochastic linear-quadratic control problem is introduced as auxiliary problem of the initial problem. In order to solve the auxiliary problem, a verification theorem for general stochastic optimal control with states following an jump-diffusion process is showed. By applying the verification theorem and solving the HJB equation, the optimal strategies in an explicit form for the auxiliary and initial control problem are presented. Finally, the efficient frontier in a closed form for the initial portfolio selection problem is derived. Copyright Springer-Verlag 2004

Suggested Citation

  • Wenjing Guo & Chengming Xu, 2004. "Optimal portfolio selection when stock prices follow an jump-diffusion process," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 485-496, December.
    • Handle: RePEc:spr:mathme:v:60:y:2004:i:3:p:485-496
    DOI: 10.1007/s001860400365
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    Citations

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    Cited by:

    1. Yu Yang & Yonghong Wu & Benchawan Wiwatanapataphee, 2020. "Time-consistent mean–variance asset-liability management in a regime-switching jump-diffusion market," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(4), pages 401-427, December.
    2. Nicole Bäuerle & Ulrich Rieder, 2013. "Optimal Deterministic Investment Strategies for Insurers," Risks, MDPI, vol. 1(3), pages 1-18, November.
    3. Wenjing Guo & Chengming Xu, 2007. "Correction on “Optimal portfolio selection when stock prices follow an jump-diffusion process”," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 559-564, June.
    4. Łukasz Delong & Russell Gerrard, 2007. "Mean-variance portfolio selection for a non-life insurance company," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 339-367, October.
    5. Ricardo Huamán-Aguilar & Abel Cadenillas, 2015. "Government Debt Control: Optimal Currency Portfolio and Payments," Operations Research, INFORMS, vol. 63(5), pages 1044-1057, October.
    6. Wei Yan & Shurong Li, 2008. "A class of portfolio selection with a four-factor futures price model," Annals of Operations Research, Springer, vol. 164(1), pages 139-165, November.
    7. Huiling Wu, 2013. "Mean-Variance Portfolio Selection with a Stochastic Cash Flow in a Markov-switching Jump–Diffusion Market," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 918-934, September.
    8. Josa-Fombellida, Ricardo & López-Casado, Paula, 2023. "A defined benefit pension plan game with Brownian and Poisson jumps uncertainty," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1294-1311.

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