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Robust utility maximisation with intractable claims

Author

Listed:
  • Yunhong Li

    (The Hong Kong Polytechnic University)

  • Zuo Quan Xu

    (The Hong Kong Polytechnic University)

  • Xun Yu Zhou

    (Columbia University)

Abstract

We study a continuous-time expected utility maximisation problem where the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the claim other than its probability distribution; hence the name “intractable claim”. In view of the lack of necessary information about the claim, we consider a robust formulation to maximise her utility in the worst scenario. We apply the quantile formulation to solve the problem, express the quantile function of the optimal terminal investment income as the solution of certain variational inequalities of ordinary differential equations, and obtain the resulting optimal trading strategy. In the case of exponential utility, the problem reduces to a (non-robust) rank-dependent utility maximisation with probability distortion whose solution is available in the literature. The results can also be used to determine the utility indifference price of the intractable claim.

Suggested Citation

  • Yunhong Li & Zuo Quan Xu & Xun Yu Zhou, 2023. "Robust utility maximisation with intractable claims," Finance and Stochastics, Springer, vol. 27(4), pages 985-1015, October.
    • Handle: RePEc:spr:finsto:v:27:y:2023:i:4:d:10.1007_s00780-023-00512-2
    DOI: 10.1007/s00780-023-00512-2
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Intractable claim; Robust model; Quantile formulation; Calculus of variations; Variational inequalities; Rank-dependent utility;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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