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Portfolio management with benchmark related incentives under mean reverting processes

Author

Listed:
  • Marco Nicolosi

    (University of Perugia)

  • Flavio Angelini

    (University of Perugia)

  • Stefano Herzel

    (University of Rome, Tor Vergata)

Abstract

We study the problem of a fund manager whose compensation depends on the relative performance with respect to a benchmark index. In particular, the fund manager’s risk-taking incentives are induced by an increasing and convex relationship of fund flows to relative performance. We consider a dynamically complete market with N risky assets and the money market account, where the dynamics of the risky assets exhibit mean reversions, either in the drift or in the volatility. The manager optimizes the expected utility of the final wealth, with an objective function that is non-concave. The optimal solution is found by using the martingale approach and a concavification method. The optimal wealth and the optimal strategy are determined by solving a system of Riccati equations. We provide a semi-closed solution based on the Fourier transform.

Suggested Citation

  • Marco Nicolosi & Flavio Angelini & Stefano Herzel, 2018. "Portfolio management with benchmark related incentives under mean reverting processes," Annals of Operations Research, Springer, vol. 266(1), pages 373-394, July.
    • Handle: RePEc:spr:annopr:v:266:y:2018:i:1:d:10.1007_s10479-017-2535-y
    DOI: 10.1007/s10479-017-2535-y
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    Cited by:

    1. Chendi Ni & Yuying Li & Peter A. Forsyth, 2023. "Neural Network Approach to Portfolio Optimization with Leverage Constraints:a Case Study on High Inflation Investment," Papers 2304.05297, arXiv.org, revised May 2023.
    2. Stefano Herzel & Marco Nicolosi, 2017. "Portfolio allocation in actively managed funds," Economics Bulletin, AccessEcon, vol. 37(3), pages 1688-1693.
    3. Constantin Mellios & Anh Ngoc Lai, 2022. "Incentive Fees with a Moving Benchmark and Portfolio Selection under Loss Aversion," Post-Print hal-03708926, HAL.
    4. Guodong Ding & Daniele Marazzina, 2021. "Effect of Labour Income on the Optimal Bankruptcy Problem," Papers 2106.15426, arXiv.org.
    5. Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "The value of knowing the market price of risk," Annals of Operations Research, Springer, vol. 299(1), pages 101-131, April.
    6. Flavio Angelini & Katia Colaneri & Stefano Herzel & Marco Nicolosi, 2021. "Implicit incentives for fund managers with partial information," Computational Management Science, Springer, vol. 18(4), pages 539-561, October.
    7. Emilio Barucci & Daniele Marazzina & Elisa Mastrogiacomo, 2021. "Optimal investment strategies with a minimum performance constraint," Annals of Operations Research, Springer, vol. 299(1), pages 215-239, April.
    8. Chen, An & Hieber, Peter & Nguyen, Thai, 2019. "Constrained non-concave utility maximization: An application to life insurance contracts with guarantees," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1119-1135.
    9. Marco Nicolosi, 2018. "Optimal strategy for a fund manager with option compensation," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(1), pages 1-17, May.
    10. Sheng, Jiliang & Xu, Si & An, Yunbi & Yang, Jun, 2021. "Dynamic portfolio strategy by loss-averse fund managers facing performance-induced fund flows," International Review of Financial Analysis, Elsevier, vol. 73(C).
    11. van Staden, Pieter M. & Forsyth, Peter A. & Li, Yuying, 2024. "Across-time risk-aware strategies for outperforming a benchmark," European Journal of Operational Research, Elsevier, vol. 313(2), pages 776-800.

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