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Optimal Investment Based on Performance Measure and Stochastic Benchmark Under PI and Position Constraints

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  • Chengzhe Wang

    (School of Mathematics, Suzhou University of Science and Technology, Suzhou 215009, China)

  • Congjin Zhou

    (School of Mathematics, Suzhou University of Science and Technology, Suzhou 215009, China)

  • Yinghui Dong

    (School of Mathematics, Suzhou University of Science and Technology, Suzhou 215009, China)

Abstract

We consider the portfolio selection problem faced by a manager under the performance ratio with position and portfolio insurance (PI) constraints. By making use of a dual control method in an incomplete market setting, we find the unique pricing kernel in the presence of closed convex cone control constraints. Then, following the same arguments as in the complete market case, we derive the explicit form of the optimal investment strategy by combining the linearization method, the Lagrangian method, and the concavification technique.

Suggested Citation

  • Chengzhe Wang & Congjin Zhou & Yinghui Dong, 2025. "Optimal Investment Based on Performance Measure and Stochastic Benchmark Under PI and Position Constraints," Mathematics, MDPI, vol. 13(11), pages 1-26, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1846-:d:1670232
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    References listed on IDEAS

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