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Utility Maximization In Affine Stochastic Volatility Models

Author

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  • JAN KALLSEN

    (Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Westring 383, 24118 Kiel, Germany)

  • JOHANNES MUHLE-KARBE

    (Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria)

Abstract

We consider the classical problem of maximizing expected utility from terminal wealth. With the help of a martingale criterion explicit solutions are derived for power utility in a number of affine stochastic volatility models.

Suggested Citation

  • Jan Kallsen & Johannes Muhle-Karbe, 2010. "Utility Maximization In Affine Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 459-477.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:03:n:s0219024910005851
    DOI: 10.1142/S0219024910005851
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    References listed on IDEAS

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    1. Ralf Korn, 1997. "Optimal Portfolios:Stochastic Models for Optimal Investment and Risk Management in Continuous Time," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3548, August.
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    Citations

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    Cited by:

    1. Richter, Anja, 2014. "Explicit solutions to quadratic BSDEs and applications to utility maximization in multivariate affine stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3578-3611.
    2. Nicole Bauerle & Sascha Desmettre, 2018. "Portfolio Optimization in Fractional and Rough Heston Models," Papers 1809.10716, arXiv.org, revised May 2019.
    3. Branger, Nicole & Muck, Matthias & Seifried, Frank Thomas & Weisheit, Stefan, 2017. "Optimal portfolios when variances and covariances can jump," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 59-89.
    4. Jingtang Ma & Wenyuan Li & Harry Zheng, 2017. "Dual control Monte Carlo method for tight bounds of value function under Heston stochastic volatility model," Papers 1710.10487, arXiv.org.
    5. M. Escobar-Anel & M. Kschonnek & R. Zagst, 2023. "Mind the cap!—constrained portfolio optimisation in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 23(12), pages 1793-1813, November.
    6. Frank Bosserhoff & An Chen & Nils Sorensen & Mitja Stadje, 2021. "On the Investment Strategies in Occupational Pension Plans," Papers 2104.08956, arXiv.org.
    7. Marcos Escobar-Anel & Yevhen Havrylenko & Rudi Zagst, 2022. "Value-at-Risk constrained portfolios in incomplete markets: a dynamic programming approach to Heston's model," Papers 2208.14152, arXiv.org, revised Jul 2024.
    8. Di Nunno, Giulia & Sjursen, Steffen, 2014. "BSDEs driven by time-changed Lévy noises and optimal control," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1679-1709.
    9. Ariel Neufeld & Marcel Nutz, 2015. "Robust Utility Maximization with L\'evy Processes," Papers 1502.05920, arXiv.org, revised Mar 2016.
    10. Sascha Desmettre & Sebastian Merkel & Annalena Mickel & Alexander Steinicke, 2023. "Worst-Case Optimal Investment in Incomplete Markets," Papers 2311.10021, arXiv.org.
    11. Nicole Bäuerle & Tamara Göll, 2023. "Nash equilibria for relative investors via no-arbitrage arguments," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(1), pages 1-23, February.
    12. Yang Shen, 2020. "Effect of Variance Swap in Hedging Volatility Risk," Risks, MDPI, vol. 8(3), pages 1-34, July.
    13. Yumo Zhang, 2023. "Utility maximization in a stochastic affine interest rate and CIR risk premium framework: a BSDE approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 97-128, June.
    14. Zongxia Liang & Ming Ma, 2020. "Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1035-1072, July.
    15. Kraft, Holger & Meyer-Wehmann, André & Seifried, Frank Thomas, 2020. "Dynamic asset allocation with relative wealth concerns in incomplete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).

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