Contracting for Innovation under Ambiguity
At any given point in time, the collection of assets that exist in the economy is observable. Each asset is a function of a set of contingencies. The union taken over all assets of these contingencies is what we call the set of publicly known states. An innovation is a set of states that are not publicly known along with an asset (in a broad sense) that pays contingent on those states. The creator of an innovation is an entrepreneur. He is represented by a probability measure on the set of new states. All other agents perceive the innovation as ambiguous: each of them is represented by a set of probabilities on the new states. The agents in the economy are classified with respect to their attitude toward the Ambiguity: the financiers are (locally) ambiguity seeking while the consumers are ambiguity averse. An entrepreneur and a financier come together when the former seeks funds to implement his project and the latter seeks new profit opportunities. The resulting contracting problem does not fall within the standard theory due to the presence of Ambiguity (on the financier's side) and to the heterogeneity in the parties' beliefs. We prove existence and monotonicity (i.e., truthful revelation) of the optimal contract. We characterize this contract under the additional assumption that the financiers are globally ambiguity seeking. Finally, we re-formulate our results in an insurance framework and extend the classical result of Arrow-Borch-Raviv and the more recent one of Ghossoub. In the case of an Ambiguity averse insurer, we also show that the optimal contract has the form of a generalized deductible.
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