Arrow's theorem of the deductible with heterogeneous beliefs

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      <subfield code="a">Ghossoub, Mario</subfield>
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      <subfield code="a">Arrow's theorem of the deductible with heterogeneous beliefs</subfield>
      <subfield code="c">Mario Ghossoub</subfield>
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      <subfield code="a">In Arrow¿s classical problem of demand for insurance indemnity schedules, it is well-known that the optimal insurance indemnification
for an insurance buyeror decision maker (DM)is a deductible contract when the insurer is a risk-neutral Expected-Utility (EU)
maximizer and when the DM is a risk-averse EU maximizer. In Arrow¿s framework, however, both parties share the same probabilistic
beliefs about the realizations of the underlying insurable loss. This article reexamines Arrow¿s problem in a setting where the DM and
the insurer have different subjective beliefs. Under a requirement of compatibility between the insurer¿s and the DM¿s subjective beliefs,
we show the existence and monotonicity of optimal indemnity schedules for the DM. The belief compatibility condition is shown to be a
weakening of the assumption of a monotone likelihood ratio. In the latter case, we show that the optimal indemnity schedule is a variable
deductible schedule, with a state-contingent deductible that depends on the state of the world only through the likelihood ratio. Arrow¿s
classical result is then obtained as a special case.</subfield>
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      <subfield code="a">Cálculo actuarial</subfield>
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      <subfield code="a">Probabilidad de impago</subfield>
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      <subfield code="0">MAPA20080602437</subfield>
      <subfield code="a">Matemática del seguro</subfield>
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      <subfield code="w">MAP20077000239</subfield>
      <subfield code="t">North American actuarial journal</subfield>
      <subfield code="d">Schaumburg : Society of Actuaries, 1997-</subfield>
      <subfield code="x">1092-0277</subfield>
      <subfield code="g">01/03/2017 Tomo 21 Número 1 - 2017 , p. 15-35</subfield>
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