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A class of portfolio optimization solvable problems

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  • Cheng, Yuyang
  • Escobar-Anel, Marcos

Abstract

This short paper reveals the largest class of stochastic volatility processes solvable in closed form within expected utility theory for a hyperbolic absolute risk aversion investor. The risky-asset setting considers a framework outside the seminal work of Liu (2007), and highlights applications not yet studied in the literature. The work also demonstrates that analytical solutions for ambiguity-aversion analyses within the framework of Maenhout (2004) are feasible.

Suggested Citation

  • Cheng, Yuyang & Escobar-Anel, Marcos, 2023. "A class of portfolio optimization solvable problems," Finance Research Letters, Elsevier, vol. 52(C).
    • Handle: RePEc:eee:finlet:v:52:y:2023:i:c:s1544612322005505
    DOI: 10.1016/j.frl.2022.103373
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    References listed on IDEAS

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    1. George Chacko & Luis M. Viceira, 2005. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1369-1402.
    2. Legendre, François & Togola, Djibril, 2016. "Explicit solutions to dynamic portfolio choice problems: A continuous-time detour," Economic Modelling, Elsevier, vol. 58(C), pages 627-641.
    3. Yumo Zhang, 2021. "Dynamic Optimal Mean-Variance Portfolio Selection with a 3/2 Stochastic Volatility," Risks, MDPI, vol. 9(4), pages 1-21, March.
    4. Yumo Zhang, 2021. "Dynamic Optimal Mean-Variance Investment with Mispricing in the Family of 4/2 Stochastic Volatility Models," Mathematics, MDPI, vol. 9(18), pages 1-25, September.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Li, Zhongfei & Zeng, Yan & Lai, Yongzeng, 2012. "Optimal time-consistent investment and reinsurance strategies for insurers under Heston’s SV model," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 191-203.
    7. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    8. 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.
    9. Yuyang Cheng & Marcos Escobar-Anel, 2021. "Optimal investment strategy in the family of 4/2 stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 21(10), pages 1723-1751, October.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Holger Kraft, 2005. "Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 303-313.
    15. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    16. Martino Grasselli, 2017. "The 4/2 Stochastic Volatility Model: A Unified Approach For The Heston And The 3/2 Model," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 1013-1034, October.
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