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Systems of ergodic BSDEs arising in regime switching forward performance processes

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Listed:
  • Ying Hu
  • Gechun Liang
  • Shanjian Tang

Abstract

We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called \emph{ergodic BSDE systems}. Such systems arise naturally as candidate solutions to characterize forward performance processes and their associated optimal trading strategies in a regime switching market. In addition, we develop a connection between the solution of the ergodic BSDE system and the long-term growth rate of classical utility maximization problems, and use the ergodic BSDE system to study the large time behavior of PDE systems with quadratic growth Hamiltonians.

Suggested Citation

  • Ying Hu & Gechun Liang & Shanjian Tang, 2018. "Systems of ergodic BSDEs arising in regime switching forward performance processes," Papers 1807.01816, arXiv.org, revised Jun 2020.
    • Handle: RePEc:arx:papers:1807.01816
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    References listed on IDEAS

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    1. Dmitry Kramkov & Sergio Pulido, 2014. "A system of quadratic BSDEs arising in a price impact model," Papers 1408.0916, arXiv.org, revised May 2016.
    2. Dmitry Kramkov & Sergio Pulido, 2016. "Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model," Post-Print hal-01181147, HAL.
    3. M. Musiela & T. Zariphopoulou, 2009. "Portfolio choice under dynamic investment performance criteria," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 161-170.
    4. Dmitry Kramkov & Sergio Pulido, 2016. "Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model," Working Papers hal-01181147, HAL.
    5. Wing Fung Chong & Ying Hu & Gechun Liang & Thaleia Zariphopoulou, 2019. "An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior," Finance and Stochastics, Springer, vol. 23(1), pages 239-273, January.
    6. Dmitry Kramkov & Sergio Pulido, 2016. "A system of quadratic BSDEs arising in a price impact model," Post-Print hal-01147411, HAL.
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    12. Dmitry Kramkov & Sergio Pulido, 2014. "Stability and analytic expansions of local solutions of systems of quadratic BSDEs with applications to a price impact model," Papers 1410.6144, arXiv.org, revised Aug 2016.
    13. Ying Hu & Gechun Liang & Shanjian Tang, 2017. "Exponential utility maximization and indifference valuation with unbounded payoffs," Papers 1707.00199, arXiv.org, revised Jul 2018.
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    Cited by:

    1. Gechun Liang & Yifan Sun & Thaleia Zariphopoulou, 2023. "Representation of forward performance criteria with random endowment via FBSDE and application to forward optimized certainty equivalent," Papers 2401.00103, arXiv.org.
    2. Ying Hu & Xiaomin Shi & Zuo Quan Xu, 2022. "Optimal consumption-investment with coupled constraints on consumption and investment strategies in a regime switching market with random coefficients," Papers 2211.05291, arXiv.org.
    3. Gechun Liang & Moris S. Strub & Yuwei Wang, 2021. "Predictable Forward Performance Processes: Infrequent Evaluation and Applications to Human-Machine Interactions," Papers 2110.08900, arXiv.org, revised Dec 2023.
    4. Gechun Liang & Moris S. Strub & Yuwei Wang, 2023. "Predictable Relative Forward Performance Processes: Multi-Agent and Mean Field Games for Portfolio Management," Papers 2311.04841, arXiv.org, revised Dec 2023.
    5. Juan Li & Wenqiang Li & Gechun Liang, 2020. "A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models," Papers 2005.10660, arXiv.org, revised May 2021.

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