Agency Models Based On Subadditive Measures With Applications

Principal agent problems widely exist in economic and management fields alongwith multiple types of incomplete information, which are usually caused by variouskinds of uncertain factors. However, incomplete information often has adverse im-pacts on the optimal utilities of the principal and the agent. To minimize the adverseeffects, the optimal contract should be signed between the principal and the agent toregulate their respective expected activities, while an ex-ante incentive is offered tothe agent via such an optimal contract. Therefore, seeking for the influencing factorsand designing the optimal contract under incomplete information have gradually beena heated research area.Incomplete information is usually influenced by various kinds of subjective be-liefs based on human thinking. Moreover, Ellsberg paradox showed that, in some cer-tain situations, decision makers make choices that are incompatible with any decisionrule based on probability measure. For these reasons, this dissertation characterizessuch incomplete information by the subadditive credibility measure and uncertaintymeasure. Following that, this dissertation respectively investigates the principal a-gent problems with private information and common unknown information, and thenanalyzes the impacts of the participators’ attitudes toward risk and the diversity of in-complete information on the optimal contracts. The main contents researched in thisdissertation are as follows:1) Based on credibility measure, this dissertation discusses the agency problemwith private information about the agent’s ability. The agent’s ability is unobservableto the principal, so the principal’s assessment about it is described as a fuzzy variable.To induce the agent to make the optimal decisions, the fuzzy agency model with pri-vate information is developed by designing the optimal transfer payment on the basisof the agent’s ability. By solving the proposed model, the optimal contracts are re-spectively presented when the principal is risk-averse and risk-neutral, and then theeffects of the principal’s attitude toward risk on the optimal contracts are analyzed indetail. In this case, due to the advantage in information, the agent can capture some information rent from the principal, but his subjective attitude toward risk has no effecton the optimal contract. Furthermore, to demonstrate the effectiveness, the proposedfuzzy agency model is applied to optimize the purchasing contract problem, and thenumerical results show that the optimal contract can successfully inspire the agent toreveal his private information.2) Based on credibility measure, this dissertation investigates the agency problemwith common unknown information about the agent’s ability. The principal and theagent are in the same state of information, so the most important thing for the two par-ticipators is to explore the agent’s potential ability as much as possible by cooperatingactively with each other, thus achieving a win-win outcome. To seek for the optimalcontract, the fuzzy agency model with common unknown information is establishedby designing the optimal transfer payment in accordance with the income producedby the agent. By solving the proposed model, the optimal contracts are respectivelypresented when the agent is risk-averse and risk-neutral, and then the impacts of theagent’s attitude toward risk on the optimal contracts are analyzed. The conclusionssuggest that the agent no longer has the extra ability to capture information rent fromthe principal, and the participators’ attitudes toward risk have no effect on the optimalcontract. To demonstrate the advantages and differences, the optimal contract underprivate information is compared with that under common unknown information.3) Based on uncertainty measure, this dissertation studies the agency problemwith multiple types of common unknown information to explore the impacts of theagent’s different decision rules on the optimal contract. The common unknown infor-mation is objective and unobservable, so the agent’s assessments about multiple typesof unknown information are described as independent uncertain variables. This disser-tation focuses on the optimal contracts in two situations, in which the principal makesthe optimal decision based on the expected income while the agent successively basedon the expected income and the potential income under his acceptable confidence lev-el. Following that, two classes of uncertain agency models are formulated in such twosituations, and then the sufficient and necessary conditions for the optimal contractsare proved under some certain assumptions. Furthermore, the validity of the proposedwork is supported with the numerical results in a portfolio selection problem. Theproposed results also demonstrate that the optimal contracts differ from each other due to the agent’s different decision rules, and the diversity of incomplete informationenhances the complexity of the optimal contracts. Finally, the two proposed uncertainagency models are compared with each other to illustrate the differences between themand their respective influencing factors.4) Based on uncertainty measure, this dissertation discusses the agency problemwith multiple types of common unknown information to explore the optimal contractswhen the agent’s effort is observable and unobservable to the principal, respectively.If the agent’s effort is observable, then the principal ensures the agent’s willingnessto cooperate with him by the participation constraint. However, if the agent’s effortis unobservable to the principal, then the optimal contract depends on whether theagent is willing to share the potential risk with the principal. According to the agent’sdifferent requests, three classes of uncertain agency models are successively developedon the basis of the two individuals’ acceptable confidence levels, which quantify thedegrees of the two participators’ risk aversions. Following that, the optimal contractsare respectively presented with the detailed proofs, and the uniqueness and complexityof each optimal contract are analyzed. Finally, the validity of the proposed work isfurther supported with the numerical results in a portfolio selection problem.5) The main contents researched in this dissertation are compared with the rele-vant existing work. Firstly, the proposed work about fuzzy agency model and uncer-tain agency model is compared with the relevant literature, respectively. Secondly, theagency models based on credibility measure and uncertainty measure are comparedwith that based on probability measure, respectively. The comparative results not onlyshow the main innovations and contributions in this research, but also verify the fea-sibility and validity of credibility measure and uncertainty measure to be applied todeal with agency problems under incomplete information. Moreover, the comparativeresults provide the guidance for decision makers to identify the most suitable solutionmethod according to each specific agency problem.