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Optimal contracting under mean-volatility joint ambiguity uncertainties

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  • Jaeyoung Sung

    (Ajou University)

Abstract

We examine a continuous-time principal-agent problem under mean-volatility joint ambiguity uncertainties. Both the principal and the agent exhibit Gilboa–Schmeidler’s extreme ambiguity aversion with exponential utilities. We distinguish between expost realized and exante perceived volatilities, and argue that the second-best contract necessarily consists of two sharing rules: one for realized outcome and the other for realized volatility. The outcome-sharing rule is for uncertainty sharing and work incentives, as usual, and the volatility-sharing rule is to align the agent’s worst prior with that of the principal. At optimum, their worst priors are symmetrized, and realized compensation is positively related to realized volatility. This theoretical positive relation can be consistent with popular managerial compensation practices such as restricted stock plus stock option grants. A closed-form solution to a linear-quadratic example is provided.

Suggested Citation

  • Jaeyoung Sung, 2022. "Optimal contracting under mean-volatility joint ambiguity uncertainties," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 593-642, September.
    • Handle: RePEc:spr:joecth:v:74:y:2022:i:2:d:10.1007_s00199-021-01362-9
    DOI: 10.1007/s00199-021-01362-9
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    2. Jianjun Miao, 2022. "Introduction to the special issue in honor of Larry Epstein," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 329-333, September.

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    More about this item

    Keywords

    Mean-volatility ambiguity; Perception asymmetry; Moral hazard; Optimal contract; Stock option; Managerial compensation; Volatility control;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G34 - Financial Economics - - Corporate Finance and Governance - - - Mergers; Acquisitions; Restructuring; Corporate Governance

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