Continuous-time contracting problems with one-sided limited commitment under Knightian uncertainty

doi:10.3969/j.issn.0253-2778.2020.02.010

Abstract

Abstract: The optimal contract design problem with one-sided limited commitment under Knightian uncertainty was studied.First，based on the agent’s endowment process and the consumption returned by the principal under Knightian uncertainty，the contract model was established with the agent’s one-side limited commitment which characterizes the maximization of the principal expected profit under the agent’s expected utility (the agent’s continuation value) being not lower than the agent’s outside option value (keeping the participation constraint).By using the dynamic programming principle under Peng’s sublinear expectation theory， the Hamilton-Jacobi-Bellman (HJB) equation of the principal’s value function on her maximal expected utility was derived.Next，using the sublinear theory， the weak and strong dual theorems and the verification theorem of optimal strategy were obtained.Finally，for an example of consumption，the numerical simulation for results and the corresponding economic analysis were provided.

Key words: Knightian uncertainty, sublinear expectation, continuous-time contracts, one-sided limited commitment, HJB equation

CLC Number:

FEI Weiyin,YANG Shanshan,LIANG Yong. Continuous-time contracting problems with one-sided limited commitment under Knightian uncertainty[J]. Journal of University of Science and Technology of China, 2020, 50(2): 146-155.

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