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Optimal contract for a fund manager, with capital injections and endogenous trading constraints

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  • Sergey Nadtochiy
  • Thaleia Zariphopoulou

Abstract

In this paper, we construct a solution to the optimal contract problem for delegated portfolio management of the fist-best (risk-sharing) type. The novelty of our result is (i) in the robustness of the optimal contract with respect to perturbations of the wealth process (interpreted as capital injections), and (ii) in the more general form of principals objective function, which is allowed to depend directly on the agents strategy, as opposed to being a function of the generated wealth only. In particular, the latter feature allows us to incorporate endogenous trading constraints in the contract. We reduce the optimal contract problem to the following inverse problem: for a given portfolio (defined in a feedback form, as a random field), construct a stochastic utility whose optimal portfolio coincides with the given one. We characterize the solution to this problem through a Stochastic Partial Differential Equation (SPDE), prove its well-posedness, and compute the solution explicitly in the Black-Scholes model.

Suggested Citation

  • Sergey Nadtochiy & Thaleia Zariphopoulou, 2018. "Optimal contract for a fund manager, with capital injections and endogenous trading constraints," Papers 1802.09165, arXiv.org.
  • Handle: RePEc:arx:papers:1802.09165
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    References listed on IDEAS

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    1. Suleyman Basak & Anna Pavlova & Alexander Shapiro, 2007. "Optimal Asset Allocation and Risk Shifting in Money Management," Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1583-1621, 2007 21.
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    3. Starks, Laura T., 1987. "Performance Incentive Fees: An Agency Theoretic Approach," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(1), pages 17-32, March.
    4. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    5. Hui Ou-Yang, 2003. "Optimal Contracts in a Continuous-Time Delegated Portfolio Management Problem," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 173-208.
    6. Cadenillas, Abel & Cvitanic, Jaksa & Zapatero, Fernando, 2007. "Optimal risk-sharing with effort and project choice," Journal of Economic Theory, Elsevier, vol. 133(1), pages 403-440, March.
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    Cited by:

    1. Xue Dong He & Moris S. Strub & Thaleia Zariphopoulou, 2019. "Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability Distortion," Papers 1904.01745, arXiv.org.

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