Research On Moral Hazard Problems Under Fuzzy Environments

By the mere fact of delegation, the principal can only observe the agent'sproduction level a?ected by the agent's action such as e?ort level and the state ofnature, since the agent's behavior can not be veri?ed after signing the contract.Therefore, it is possible for the agent to have an incentive to behave inappropri-ately from the perspective of the principal. This phenomenon is called existingmoral hazard with hidden action, which is an important part of the principal-agent theory.However, in reality, the principal may give a subjective assessment of thestate of nature or the production level according to insu?cient historical dateand his/her own experience. This provides a motivation for the thesis to usefuzzy variables to denote these uncertain environments or the production level.First, the thesis establishes a fuzzy parameterized expected value model,in which a fuzzy variable is denoted as the agent's production level. And thismodel aims to maximize the expected utility of the principal under the incentivecompatibility constraints and the participation constraint. To solve the proposedmodel, credibility theory is adopted to convert the fuzzy expected value modelinto an optimal control problem at ?rst, and then Pontryagin maximum principleis used to give necessary conditions for the existence of solution. Finally, speci?cexamples are given to illustrate the idea of modeling.In addition, the thesis formulates a fuzzy state-space model about the moralhazard, in which a fuzzy variable is denoted as the state of nature. In thismodel, how the agent's action and the state of nature a?ect the result of theagent's action are demonstrated very intuitively, which is helpful for the profoundunderstanding of moral hazard. Combining with speci?c examples, the methodused in the third chapter is also applicable.