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Moral hazard is a key issue in principal-agent literature. Examples lie in several aspects of real life, such as the worker´s lack of effort when his/her conduct cannot be directly observed by the employer, and the principal´s consequent need to motivate the agent to work as much as possible in his/her best interests. Another example is the relationship between voters and politicians, where elections serve as a disciplining mechanism to prevent rent-seeking behavior by unobserved public administrators. In this work we analyze such problems in a continuous-time setting with a model specification that draws from the classical consumption/investment à la Merton. Agents differ in competence, which is incompletely (but symmetrically) known by all players and learned over time by observing agent´s performance. From a mathematical point of view, the analysis uses classical filtering techniques to re-formulate the problem within a complete information setting; then, relying on the dynamic programming principle and by using a guess-and-verify approach, explicit (at least to some extent) solutions are provided.

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Alessandra Mainini, Ph.D in Economics, is research fellow at Università Cattolica del Sacro Cuore (Milano, Italy). Her research interests are in the fields of applied stochastic control and filtering.

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