Optimal contracts for the agency problem with multiple uncertain information

There is usually such a kind of agency problem where one principal authorizes one agent to perform more than one task at the same time. However, the potential output of each task cannot be exactly predicted in advance, so there exist simultaneously multiple types of uncertain information about the potential outputs of all the tasks. In this case, how to design the optimal contract and how to investigate the impacts of the diversity of uncertain information on such an optimal contract become important and challenging for decision makers. Motivated by this, to filter out the uncertainty in the possible incomes, we firstly focus on the optimal contract when both the two participators’ potential incomes are measured by their respective expected incomes. Following that, as an important innovation, confidence level is introduced to quantify the degree of the agent’s risk aversion, and the effects of the agent’s attitude toward risk on the optimal contract and the principal’s income are taken into account. Based on this view, two classes of uncertain agency models are developed, and then the sufficient and necessary conditions for the optimal contracts are presented with the detailed proofs and analyses. Compared with the traditional agency model, the innovations and advantages of the proposed work are briefly summarized, and the effectiveness of the work is further demonstrated by the computational results in a portfolio selection problem.