An optimal insurance design problem under Knightian uncertainty

This paper solves an optimal insurance design problem in which both the insurer and the insured are subject to Knightian uncertainty about the loss distribution. The Knightian uncertainty is modeled in a multi-prior g-expectation framework. We obtain an endogenous characterization of the optimal indemnity that extends classical theorems of Arrow (Essays in the Theory of Risk Bearing. Markham, Chicago <CitationRef CitationID="CR2">1971</CitationRef>) and Raviv (Am Econ Rev 69(1):84–96, <CitationRef CitationID="CR48">1979</CitationRef>) in the classical situation. In the presence of Knightian uncertainty, it is shown that the optimal insurance contract is not only contingent on the realized loss but also on another source of uncertainty coming from the ambiguity. Copyright Springer-Verlag 2013