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G-expected utility maximization with ambiguous equicorrelation

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  • Chi Seng Pun

Abstract

This paper studies a class of expected utility maximization problems with respect to a controlled state process with multiple noises, whose pairwise correlations are equal and ambiguous. Using the G-expectation theory, we solve for the robust stochastic controls explicitly from a Hamilton–Jacobi–Bellman–Isaacs equation and deduce a robust choice of the equicorrelation coefficient. We also generalize the results to a block equicorrelation structure, where we consider more than two ambiguous parameters that could be interactive in general. We manage to derive an analytical solution to the robust stochastic controls under an ambiguous two-block equicorrelated structure via the solution to a system of polynomial equations. The results have significant implications for the investment and reinsurance problems among many others.

Suggested Citation

  • Chi Seng Pun, 2021. "G-expected utility maximization with ambiguous equicorrelation," Quantitative Finance, Taylor & Francis Journals, vol. 21(3), pages 403-419, March.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:3:p:403-419
    DOI: 10.1080/14697688.2020.1777321
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    Cited by:

    1. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2021. "Duality theory for robust utility maximisation," Finance and Stochastics, Springer, vol. 25(3), pages 469-503, July.
    2. Chi Seng Pun, 2022. "Robust classical-impulse stochastic control problems in an infinite horizon," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(2), pages 291-312, October.
    3. Bingyan Han & Chi Seng Pun & Hoi Ying Wong, 2021. "Robust state-dependent mean–variance portfolio selection: a closed-loop approach," Finance and Stochastics, Springer, vol. 25(3), pages 529-561, July.

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